Help:Rotationen mit Quaternionen (Einführung in die Quaternionen-Mathematik)

Im Jahr 1843 erarbeitete Sir William Rowan Hamilton ein vierdimensionales Zahlensystem samt zugehöriger Algebra, das er als Quaternionen (lat. quaternio: „Vierheit“) bezeichnete. Die Quaternionen verstehen sich als Erweiterung der reellen Zahlen um drei weitere Dimensionen. Quaternionen finden häufig Verwendung bei der Beschreibung von Drehungen im dreidimensionalen Raum, z.B. in der Computergrafik oder in Reglern und Simulationen in Luft- und Raumfahrt. Sie bieten eine sehr elegante Möglichkeit, Drehungen im dreidimensionalen Raum zu beschreiben und Nachteile von Matrixtransformationen zu umgehen.

Zunächst mag es erstaunlich und vielleicht auch abschreckend sein, sich einer vierdimensionalen Algebra bei der Beschreibung von Transformationen in einem dreidimensionalen Raum zu bedienen, zumal Quaternionen vielfach nicht Inhalt der Lehre während der mathematischen Grundausbildung an Hochschulen und Universitäten sind. Ich möchte daher auf dieser Seite versuchen, einen kurzen, praktisch orientierten Einblick in den Körper der Quaternionen zu geben und auf die Vor- und Nachteile der Quaternionen und Rotationsmatrizen/Matrixtransformationen einzugehen. Diese Einführung legt dabei bewusst Hauptaugenmerk auf die Verwendung von Beispielen, um den Einstieg in die Thematik zu erleichtern.

Elementare Transformationen von Punkten im dreidimensionalen Raum

Ein Vektor <math>\vec{P} \in \mathbb{R}^3</math> soll den Ortsvektor eines Punktes im dreidimensionalen Raum (<math>\mathbb{R}^3</math>) in kartesischen Koordinaten beschreiben. Der Vektor <math>\vec{P}</math> besteht aus den Komponenten

<math>\vec{P} = \begin{pmatrix} P_x \\ P_y \\ P_z \end{pmatrix}</math>     mit <math>P_x, P_y, P_z \in \mathbb{R}.</math>

miniatur|rechts|300px|Ein Punkt im dreidimensionalen Raum <math>\mathbb{R}^3</math>. Das Schaubild zeigt die Zerlegung seines Ortsvektors <math>\vec{P}</math> in seine Komponenten <math>P_x</math>, <math>P_y</math> und <math>P_z</math>.

Dieser Punkt kann nun verändert (transformiert) werden; dabei entsteht ein neuer, transformierter Punkt <math>\vec{P}^\star \in \mathbb{R}^3</math> mit <math>\vec{P}^\star = \begin{pmatrix} P_x^\star \\ P_y^\star \\ P_z^\star \end{pmatrix}</math>. Folgende Transformationen des Ursprungspunktes <math>\vec{P}</math> sind beispielsweise denkbar:

• Verschiebung (Translation)
• Drehung um eine Rotationsachse (Rotation)
• Spiegelung
• Projektion auf eine Koordinatenebene (x-y-, y-z- oder x-z-Ebene).

Spricht man nicht nur von einem einzelnen Punkt <math>\vec{P}</math>, sondern von einer Menge <math>\mathcal{P}</math> von Punkten <math>\vec{P}_i</math> und damit von einem Objekt, z.B. den Eckpunkten eines Quaders, so sind folgende zusätzliche Transformationen denkbar:

• Scherung/Deformation
• (dimensionsweise) Vergrößerung/Verkleinerung (Skalierung)
• perspektivische Transformation.

An dieser Stelle soll nun jedoch lediglich die Rotation näher betrachtet werden.

Drehung um eine Rotationsachse mit einer Rotationsmatrix

Gegeben sei ein Punkt <math>\vec{P}</math>, dessen Ortsvektor und die Abszisse des kartesischen Koordinatensystems einen beliebigen Winkel <math>\alpha \in [0, 2 \pi[</math> einschließt. Dieser Punkt <math>\vec{P}</math> soll durch Rotation um einen beliebigen Winkel <math>\varphi \in [0, 2\pi[</math> bezüglich des Koordinatenursprungs <math>\vec{o} = (0,0,0)^\mathrm{T}</math> <ref group="Anm." name="origo" /> in einen neuen Punkt <math>\vec{P}^\star</math> transformiert werden. Die Rotation wird um die Applikate (z-Achse) durchgeführt. Die nebenstehende Abbildung veranschaulicht diesen Sachverhalt.

miniatur|350px|rechts|Grafik zur Herleitung der Rotationsmatrix <math>\underline{R_z}</math>

Man kann nun feststellen, dass unendliche viele, voneinander verschiedene Rotationen des Punktes <math>\vec{P}</math> um die Applikate transformierte Punkte <math>\vec{P}_i^\star</math> erzeugen, die sich auf einem Kreis mit Mittelpunkt <math>\vec{o}</math> und einem Radius <math>r = \sqrt{P_x^2 + P_y^2}</math> (dem Abstand des Punktes <math>\vec{P}</math> zur Applikate) sammeln.

Aus den trigonometrischen Funktionen ergeben sich die Koordinaten für den Ursprungspunkt <math>\vec{P}</math> wie folgt (die dritte Komponente bleibt unberührt):

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 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: hundreds

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  tens
   

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: hundreds

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}} }}}}}|}}

thin solid|none}}; padding:0.08em;" nowrap| 1

thin solid|none}}; padding:0.08em;"| thin solid|none}}; padding:0.08em;" rowspan="2"|   thin solid|none}}; padding:0.08em;"|   thin solid|none}}; padding:0.08em;" rowspan="2"|   thin solid|none}}; border-top:0px none #e5e5e5; border-right:{{#if:|thin solid|none}}; border-bottom:{{#if:|thin solid|none}}; padding:0.08em;"|

thin solid|none}}; padding:0.08em;" nowrap| {{#if:|{{{3}}}|({{{3}}})}}

{{#if::|{{{{{safesubst:#ifeq: x{{safesubst:#if:x|:}} | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000:

| 500 | {{safesubst:#switch: ones

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  tens
   

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: hundreds

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: tens

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: hundreds

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  tens
   

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: hundreds

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}} }}}}}|}}

Ebenso ergeben sich die Koordinaten des transformierten Punktes <math>\vec{P}^\star</math> unter Zuhilfenahme der Additionstheoreme der trigonometrischen Funktionen zu

{{#if::|{{{{{safesubst:#ifeq: x{{safesubst:#if:x|:}} | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000: | 500 | {{safesubst:#switch: ones

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  tens
   

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: hundreds

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: tens

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: hundreds

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  tens
   

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: hundreds

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}} }}}}}|}}

thin solid|none}}; padding:0.08em;" nowrap| {{{2}}}

thin solid|none}}; padding:0.08em;"| thin solid|none}}; padding:0.08em;" rowspan="2"|   thin solid|none}}; padding:0.08em;"|   thin solid|none}}; padding:0.08em;" rowspan="2"|   thin solid|none}}; border-top:0px none #e5e5e5; border-right:{{#if:|thin solid|none}}; border-bottom:{{#if:|thin solid|none}}; padding:0.08em;"|

thin solid|none}}; padding:0.08em;" nowrap| {{#if:|{{{3}}}|({{{3}}})}}

{{#if::|{{{{{safesubst:#ifeq: x{{safesubst:#if:x|:}} | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000:

| 500 | {{safesubst:#switch: ones

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  tens
   

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: hundreds

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: tens

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: hundreds

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  tens
   

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: hundreds

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}} }}}}}|}} \begin{pmatrix} r (\cos \alpha \cos \varphi - \sin \alpha \sin \varphi ) \\ r (\sin \alpha \cos \varphi + \cos \alpha \sin \varphi) \\ P_z \end{pmatrix}.\end{align}</math>|2}}

Setzt man nun die beiden ersten Komponenten von <math>\vec{P}</math> aus Gleichung (1), d.h. <math>r \cos \alpha = P_x</math> und <math>r \sin \alpha = P_y</math> in Gleichung (2) ein, so ergibt sich folgende Gleichung:

{{#if::|{{{{{safesubst:#ifeq: x{{safesubst:#if:x|:}} | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000: | 500 | {{safesubst:#switch: ones

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  tens
   

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: hundreds

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: tens

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: hundreds

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  tens
   

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: hundreds

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}} }}}}}|}}

thin solid|none}}; padding:0.08em;" nowrap| 3

thin solid|none}}; padding:0.08em;"| thin solid|none}}; padding:0.08em;" rowspan="2"|   thin solid|none}}; padding:0.08em;"|   thin solid|none}}; padding:0.08em;" rowspan="2"|   thin solid|none}}; border-top:0px none #e5e5e5; border-right:{{#if:|thin solid|none}}; border-bottom:{{#if:|thin solid|none}}; padding:0.08em;"|

thin solid|none}}; padding:0.08em;" nowrap| {{#if:|{{{3}}}|({{{3}}})}}

{{#if::|{{{{{safesubst:#ifeq: x{{safesubst:#if:x|:}} | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000:

| 500 | {{safesubst:#switch: ones

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  tens
   

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: hundreds

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

  | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
  | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: tens

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: {{safesubst:#switch: hundreds

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000{{safesubst:#if:x|:}}
     | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000{{safesubst:#if:x|:}}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 9
           | 8
           }}
         | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x0000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
           | 7
           | 6
           }}
         }}
       | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x00000000000000000000000000000{{safesubst:#if:x|:}}
         | 5
         | 4
         }}
       }}
     | 3
     }}
   | 2
   }}
 | 1
 }}

| {{safesubst:#if: |0}} }}

| ones =

{{

safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}{{ safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 9
     | 8
     }}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
     | 7
     | 6
     }}
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 5
   | 4
   }}
 }}

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 3
   | 2
   }}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x{{safesubst:#if:x|:}}
   | 1
   | 0
   }}
 }}

}}

}}|0}} }}

| ones =

{{safesubst:#switch:  tens
   

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

    | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
   | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
    | x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
     | 4
     | 3
     }}
   | 2
   }}
 | 1
 }}

| }}

| tens =

{{safesubst:#switch:  hundreds
     

| hundreds = {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x0000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}  

| {{safesubst:#ifeq: x{{safesubst:#if:x|:}}

      | x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
 | {{safesubst:#ifeq: x{{safesubst:#if:x|:}}
      | x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000{{safesubst:#if:x|:}}
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Man sieht leicht ein, dass Gleichung (3) auch durch eine Matrixmultiplikation<ref group="Anm." name="schema_von_falk" /><ref name="schema_von_falk1" /> einer Matrix <math>\underline{R_z} \in \mathbb{R}^{3 \times 3}</math> und dem Vektor <math>\vec{P}</math> entsteht:

Template:NumBlk

Die Matrix <math>\underline{R_z}</math> ist die Rotationsmatrix für eine Drehung um die z-Achse. Die nachfolgende Tabelle gibt einen Überblick über die elementaren Rotationsmatrizen; die Herleitung für die übrigen Achsen kann analog erfolgen. Die letzte Zeile definiert eine Rotationsmatrix für eine Drehung um eine beliebige Achse <math>\vec{n}</math>, die durch den Koordinatenursprung verläuft und deren Länge <math>\| \vec{n} \|</math> (euklidische Norm<ref group="Anm." name="euklidische_norm" />) auf 1 normiert ist. Für diese spezielle Rotationsmatrix bleibt die Herleitung aus Gründen des Umfangs an dieser Stelle aus; der geneigte Leser sei auf <ref name="3dsource" /> verwiesen.

Rotationsachse	Rotationsmatrix
x-Achse <math>(1,0,0)^\mathrm{T}</math>	<math>\underline{R_x}(\varphi) = \begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos \varphi & -\sin \varphi \\ 0 & \sin \varphi & \cos \varphi \end{pmatrix}</math>
y-Achse <math>(0,1,0)^\mathrm{T}</math>	<math>\underline{R_y}(\varphi) = \begin{pmatrix} \cos \varphi & 0 & \sin \varphi \\ 0 & 1 & 0 \\ -\sin \varphi & 0 & \cos \varphi \end{pmatrix}</math>
z-Achse <math>(0,0,1)^\mathrm{T}</math>	<math>\underline{R_z}(\varphi) = \begin{pmatrix} \cos \varphi & -\sin \varphi & 0 \\ \sin \varphi & \cos \varphi & 0 \\ 0 & 0 & 1 \end{pmatrix}</math>
\vec{n} \| = 1</math>	<math>\small \underline{R_{\vec{n}}}(\varphi) = \begin{pmatrix} \cos \varphi +n_x^2 \left(1-\cos \varphi \right) & n_x n_y \left(1-\cos \varphi \right) - n_z \sin \varphi & n_x n_z \left(1-\cos \varphi \right) + n_y \sin \varphi \\ n_y n_x \left(1-\cos \varphi \right) + n_z \sin \varphi & \cos \varphi + n_y^2\left(1-\cos \varphi \right) & n_y n_z \left(1-\cos \varphi \right) - n_1 \sin \varphi \\ n_z n_x \left(1-\cos \varphi \right) - n_y \sin \varphi & n_z n_y \left(1-\cos \varphi \right) + n_x \sin \varphi & \cos \varphi + n_z^2\left(1-\cos \varphi\right) \end{pmatrix}</math>

Beispiel

Gegeben sei ein Quader mit der Punktmenge <math>\mathcal{P}_Q = \left\{\vec{P}_1, \vec{P}_2, \ldots, \vec{P}_8\right\}</math>, wobei

<math>\vec{P}_1 = (1, -1, -1)^\mathrm{T}, \vec{P}_2 = (1, -1, 1)^\mathrm{T}, \vec{P}_3 = (1, 1, 1)^\mathrm{T}, \vec{P}_4 = (1, 1, -1)^\mathrm{T},</math>

<math>\vec{P}_5 = (-1, -1, -1)^\mathrm{T}, \vec{P}_6 = (-1, -1, 1)^\mathrm{T}, \vec{P}_7 = (-1, 1, 1)^\mathrm{T}, \vec{P}_8 = (-1, 1, -1)^\mathrm{T}</math>

die Eckpunkte des Quaders und die Verbindungsvektoren<ref group="Anm." name="verbindungsvektor" />

<math>\vec{P}_{12}, \vec{P}_{23}, \vec{P}_{34}, \vec{P}_{41}, \vec{P}_{56}, \vec{P}_{67}, \vec{P}_{78}, \vec{P}_{85}, \vec{P}_{15}, \vec{P}_{26}, \vec{P}_{37}, \vec{P}_{48}</math>

die Kanten des Quaders sind.

Anmerkungen

<references group="Anm."> <ref name="origo">Nebenbei bemerkt: <math>\small \vec{o}</math> steht für Origo (lat. „Herkunft, Ursprung“), also für die Koordinaten des Koordinatenursprungs.</ref> <ref name="schema_von_falk">Die Matrixmultiplikation kann mit dem Schema von Falk sehr einfach nachvollzogen werden. Man könnte beispielsweise folgendes Schema konstruieren:

<math>

\small \begin{array}{c|c}

    \underline{R_z} \cdot \vec{P}
   &
    \color[rgb]{0.3,0.3,0.3}
    \begin{pmatrix}
       P_x \\ P_y \\ P_z
    \end{pmatrix}

\\ \hline

    \color[rgb]{0.3,0.3,0.3}
    \begin{pmatrix}
       \cos \varphi & -\sin \varphi & 0 \\
       \sin \varphi &  \cos \varphi & 0 \\            
       0        &  0           & 1 
    \end{pmatrix}
   & 
    \color[rgb]{0.6,0,0}
    \begin{pmatrix}
       P_x \cos \varphi - P_y \sin \varphi \\
       P_x \sin \varphi + P_y \cos \varphi \\
       P_z
    \end{pmatrix}

\end{array} </math></ref> <ref name="euklidische_norm">Die euklidische Norm wird auch als 2-Norm bezeichnet.</ref> <ref name="verbindungsvektor">Der Verbindungsvektor <math>\small \vec{P}_{AB}</math> zwischen zwei Punkten <math>\small \vec{P}_A</math> und <math>\small \vec{P}_B</math> lässt sich durch Subtraktion beider Vektoren ermitteln: <math>\small \vec{P}_{AB} = \vec{P}_B - \vec{P}_A</math>.</ref> </references>