利用群论来研究魔方 - 大海Online的博客

文章灵感来源于：

https://zhuanlan.zhihu.com/p/76038006
并参考了：https://www.gap-system.org/Doc/Examples/rubik.html
使用了这里的小程序：https://www.jaapsch.net/puzzles/cubie.htm

先汇制一张，魔方图

               +--------------+
               |  1    2    3 |
               |  4  top    5 |
               |  6    7    8 |
+--------------+--------------+--------------+--------------+
|              |            8 |  8    5    3 |              |
|     left     |    front   9 |  9 right  13 |     rear     |
|              |           10 | 10   11   12 |              |
+--------------+--------------+--------------+--------------+
               |              |
               |    bottom    |
               |              |
               +--------------+      

这里做了几个简化

同一个块的两个棱或三个角，不做区分，视为同一数字
仅考虑顶部和右手边的图块，主要是顶部和8、9、10，这是我拼魔方经常研究的地方

这里仅研究，1-10 这10个块的还原方法

让我们参考 gap 的程序，来建立模型

创建一个群

gap> cube := Group((1,3,8,6)(2,5,7,4),(8,3,12,10)(5,13,11,9));
Group([ (1,3,8,6)(2,5,7,4), (3,12,10,8)(5,13,11,9) ])    

这里通过Group构造了一个群，由置换构造而来的群
- 比如：这里(1,3,8,6)的置换，表示顶部4个角块的一次置换
所以这个群，只有两元素
- 一个是(1,3,8,6)(2,5,7,4) 两个置换组合而成的TOP的转换，这里命名为 U ，（参考：http://www.rubik.com.cn/notation.htm ）
- 一个是(8,3,12,10)(5,13,11,9)，两个置换组合而成的RIGHT的转换，这里命名为 R
群里只有乘法一种运算，表示为置换的乘法
- 比如 U*U=U^2 => (1,3,8,6)(2,5,7,4) = (1,8)(3,6)(2,7)(5,4)

简化旋转的表示方法

gap> f := FreeGroup("U", "R");
<free group on the generators [ U, R ]>

gap> hom := GroupHomomorphismByImages( f, cube, GeneratorsOfGroup(f), GeneratorsOfGroup(cube) );
[ U, R ] -> [ (1,3,8,6)(2,5,7,4), (3,12,10,8)(5,13,11,9) ]

FreeGroup(“U”, “R”)是创建了两个元素的群，为了简化cube中两个元素的表示，分别代表Top、Right的旋转
GroupHomomorphismByImages是表示创建群同态，将U、R用于表示cube中定义的两个旋转

做一些测试

比如我们要实现 5、9 两个块的交换，即实现 (5,9)

gap> pre := PreImagesRepresentative(hom, (5,9));
U^-1*R*U^2*R^-1*U^-1*R*U^-1*R^-1*U^-1*R*U*R^-1*U*R*U^-2*R^-1*U*R*U^-1*R^-1*U^-2*R*U^-1*R^-1*U^-1*R*U*R^-1*U^-1

PreImagesRepresentative用于群的求解，计算出(5,9)的计算公式
答案也很好理解，比如：U、U^2、U^-1 分别表示 U的一次、两次、三次旋转
按照公式可逆旋转一次，验证一下
```
gap> v := Image(hom, pre);
(2,4)(5,9)
```
结果是 (2,4), (5,9) 两个置换，符合预期。因为(5,9)无法单独置换

在gap中使用 U、R 的转换标识

gap> U:=f.1;
gap> R:=f.2;
gap> Image(hom, R*U^-1*R^-1*U^-1*R*U^-1*R^-1*U*R*U*R^-1*U);
(1,8)(2,4)(3,6)(5,9)

可以自行构造转换方案来计算转换结果，可以用于批量验证自己的想法

然后，精彩来了…

枚举所有的转动可能

for x in cube do
    if LargestMovedPoint(x) <=7 then
        f := PreImagesRepresentative( hom, x);
        Print(LargestMovedPoint(x), " ", x, "\t===>\t", Length(f), "\t", f, "\n");
    fi;
od;    

这里我们枚举了cube中所有可能
LargestMovedPoint(x)是判断x中数字的最大值，7表示，我们只考虑1-7这7个数字转动的情况
然后进行求解公式，并打出来
Length(zz)表示求解公式的步数，几步可以转动完成

我们将看到这样的结果

()	===>	0	<identity ...>
(4,7,5)	===>	10	U^-1*R^-1*U^-1*R*U^-1*R^-1*U^-2*R*U^-1
(4,5,7)	===>	10	U*R^-1*U^2*R*U*R^-1*U*R*U
(2,5,7)	===>	10	R*U*R^-1*U*R*U^-2*R^-1*U^-2
(2,5,4)	===>	10	U*R*U*R^-1*U*R*U^-2*R^-1*U
(2,5)(4,7)	===>	18	U^-1*R*U^2*R^-1*U^-1*R*U^-1*R^-2*U^2*R*U*R^-1*U*R*U
(2,7,5)	===>	10	R^-1*U^-1*R*U^-1*R^-1*U^-2*R*U^-2
(2,7,4)	===>	20	U*R*U*R^-1*U*R*U^-2*(R^-1*U^2)^2*R*U*R^-1*U*R*U
(2,7)(4,5)	===>	20	(U*R*U*R^-1*U*R*U^-2*R^-1)^2*U^-2
(2,4,7)	===>	20	U^-1*R*U^2*R^-1*U^-1*R*U^-1*R^-1*U^-1*R*U*R^-1*U*R*U^-2*R^-1*U^-2
(2,4,5)	===>	10	U^-1*R*U^2*R^-1*U^-1*R*U^-1*R^-1*U^-1
(2,4)(5,7)	===>	20	U^-1*R*U^2*(R^-1*U^-1*R*U^-1*R^-1*U^-1)^2*U^-1*R*U^-2

举个例子
- 要转换实现(4,7,5)，这样三个棱块的转换，可以使用 U^-1*R^-1*U^-1*R*U^-1*R^-1*U^-2*R*U^-1 这个公式
- 我们使用下面的JS方法，做个转换
```
'U^-1*R^-1*U^-1*R*U^-1*R^-1*U^-2*R*U^-1'.replaceAll('*', ' ').replaceAll(/$(.*)$\^2/g, "$1 $1").replaceAll('^-1', "'").replaceAll("^2", "2").replaceAll("^-2", "2");
```
  答案是：U’ R’ U’ R U’ R’ U2 R U’ (参考 http://www.rubik.com.cn/notation.htm 这里的表示法)
- 下面是转换小工具

输入：

输出：

我们验证一下

我们使用这个工具进行验证，https://www.jaapsch.net/puzzles/cubie.htm 或者自己拿魔方验证一下， cubie 验证通过

校验更多

刚才的公式，我们挑选一部进行校验

(4,7,5) => U' R' U' R  U' R' U2 R  U'
(4,5,7) => U  R' U2 R  U  R' U  R  U
(2,7,5) =>    R' U' R  U' R' U2 R  U2
(2,5,7) =>    R  U  R' U  R  U2 R' U2
(2,5,4) => U  R  U  R' U  R  U2 R' U
(2,4,5) => U' R  U2 R' U' R  U' R' U'

(2,7,4) => U R U R' U R U2 R' U2 R' U2 2 R U R' U R U
(2,7)(4,5) => U R U R' U R U2 R' U R U R' U R U2 R' U2
(2,4)(5,7) => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U2
(2,5)(4,7) => U' R U2 R' U' R U' R2 U2 R U R' U R U

这些公式，再结合看看 http://www.rubik.com.cn/beginner2.htm ，我们能发现更多的魔方公式

再计算和校验

这里只计算了一些步数比较小的，比较有研究价值

for x in cube do
    f := PreImagesRepresentative( hom, x);
    if LargestMovedPoint(x) = 8 and Length(f) <= 10 then
        Print(LargestMovedPoint(x), " ", x, "\t===>\t", Length(f), "\t", f, "\n");
    fi;
od;

结果：

(1,6,8,3)(2,4,7,5)	===>	1	U'
(1,6,8,3)(2,4,5,7)	===>	9	U R U2 R' U' R U' R'
(1,6,8,3)(2,4)	===>	9	U R' U2 R U R' U R
(1,6,8,3)(4,7)	===>	9	R U R' U R U2 R' U
(1,6,8,3)(5,7)	===>	9	U R U R' U R U2 R'
(1,8)(2,7)(3,6)(4,5)	===>	2	U2
(1,8)(2,7,4)(3,6)	===>	10	U R U2 R' U' R U' R' U'
(1,8)(2,7,5)(3,6)	===>	10	U R' U2 R U R' U R U'
(1,8)(2,4,5)(3,6)	===>	8	R U R' U R U2 R'
(1,8)(2,4,7)(3,6)	===>	10	U R U R' U R U2 R' U'
(1,8)(3,6)(4,5,7)	===>	8	R' U' R U' R' U2 R
(1,8)(3,6)(4,7,5)	===>	8	R' U2 R U R' U R
(1,8)(2,5,4)(3,6)	===>	8	R U2 R' U' R U' R'
(1,8)(2,5,7)(3,6)	===>	10	U R' U' R U' R' U2 R U'
(1,3,8,6)(2,5,7,4)	===>	1	U
(1,3,8,6)(2,7,5,4)	===>	9	R U R' U R U2 R' U'
(1,3,8,6)(2,4)	===>	9	R' U' R U' R' U2 R U'
(1,3,8,6)(5,7)	===>	9	R U2 R' U' R U' R' U'
(1,3,8,6)(4,7)	===>	9	U' R U2 R' U' R U' R'

for x in cube do
    f := PreImagesRepresentative( hom, x);
    if LargestMovedPoint(x) = 9 then
        Print(LargestMovedPoint(x), " ", x, "\t===>\t", Length(f), "\t", f, "\n");
    fi;
od;  

举两个比较特殊的例子

  (1,3,8,6)(2,5)(4,7,9) => R U' R' U2 R U2 R'
  (1,6,8,3)(2,9,5)(4,7) => R U2 R' U2 R U  R'

计算更多可能

我们来打印出各种可能（只看1-10的变换）

for x in cube do
    f := PreImagesRepresentative( hom, x);
    if LargestMovedPoint(x) <= 10 then
        Print(x, " => ", f, "\n");
    fi;
od;

通过以下程序转换

package test;

import java.io.IOException;
import java.nio.file.Files;
import java.nio.file.Path;
import java.util.List;

public class Main {

    public static void main(String[] args) throws IOException {
        List<String> lines = Files.readAllLines(Path.of("input.txt"));
        List<String> result = lines.stream().map(s -> s.replace('*', ' ').replaceAll("\\((.+)\\)\\\\^2", "$1 $1").replace("^-1", "'").replace("^2", "2").replace("^-2", "2")).toList();
        System.out.println(String.join("\n", result));
    }
}

得到：

(5,7,9)                 => R U' R' U R U R' U U R U R' U R' U' R U' R' U2 R U'
(5,9,7)                 => U R' U2 R U R' U R U' R U' R' U' U' R U' R' U' R U R'
(4,7,9)                 => U R U R' U R U2 R' U R' U' R U' R' U2 R U' U' R U' R' U2 R U' U' R' U'
(4,7)(5,9)              => U R U R' U R U2 R' U2 R' U2 R U R' U R2 U' R' U2 R U' R' U' R U R' U'
(4,7,5)                 => U' R' U' R U' R' U2 R U'
(4,9,7)                 => U R U R' U R U2 R' U R' U' R U' R' U2 R R U' R' U2 R U' R' U' R U R'
(4,9,5)                 => U R U2 R' U2 R U R'
(4,9)(5,7)              => U R' U2 R U R' U R U R U' R' U2 R U2 R' U'
(4,5,7)                 => U R' U2 R U R' U R U
(4,5,9)                 => R U' R' U2 R U2 R' U'
(4,5)(7,9)              => U2 R U' R' U2 R U' R' U' R U R'
(3,8)(5,9,7)(6,10)      => U' R U R'
(3,8)(5,7,9)(6,10)      => R U' R' U
(3,8)(6,10)             => U R' U2 R U R' U R U' R U' R' U2 R U' R'
(3,8)(4,7)(5,9)(6,10)   => U R' U2 R U R' U R U R U' R' U
(3,8)(4,7,9)(6,10)      => R U' R2 U' R U' R' U2 R U'
(3,8)(4,7,5)(6,10)      => U2 R U' R' U2 R U' R'
(3,8)(4,5,9)(6,10)      => R' U' R U' R' U2 R U' U2 R U' R' U2 R U' R' U' R U' R' U'
(3,8)(4,5)(6,10)(7,9)   => U R U R' U R U2 R' U R' U' R U' R' U2 R U R U R'
(3,8)(4,5,7)(6,10)      => R U R' U2 R U R' U2
(3,8)(4,9,7)(6,10)      => U R' U2 R U R' U R2 U R'
(3,8)(4,9)(5,7)(6,10)   => U R U R' U R U2 R' U2 R' U2 R U R' U R2 U' R' U' U' R U' R' U' R U' R' U'
(3,8)(4,9,5)(6,10)      => U R U R' U R U R' U U R U R' U U2 R' U2 R U R' U R
(3,10,8,6)(7,9)         => R U R' U R U2 R' U R U' R' U' R U2 R' U' R U R'
(3,10,8,6)(5,7)         => R U2 R' U R U R' U' R U2 R' U' R U' R'
(3,10,8,6)(5,9)         => U R U R' U R U2 R' U R' U' R U' R' U' U' R U' R U R' U'
(3,10,8,6)(4,7,5,9)     => U' R U2 R' U' R U' R' U R U' R' U' R U' U' R' U' R U' R' U'
(3,10,8,6)(4,7,9,5)     => U R' U2 R U R' U R U2 R U R' U'
(3,10,8,6)(4,7)         => R U' R' U2 R U' R' U'
(3,10,8,6)(4,9)         => U R U R' U2 R' U' R U' R' U2 R U'
(3,10,8,6)(4,9,7,5)     => U R U R' U R U' U2 R' U' R U2 R' U' R U R'
(3,10,8,6)(4,9,5,7)     => U R U R' U'
(3,10,8,6)(4,5,7,9)     => R U R' U R U R' U' R' U' R U' R' U2 R U2 R U2 R' U' R U' R' U'
(3,10,8,6)(4,5,9,7)     => U' R U2 R' U' R U' R2 U2 R U R' U R2 U' R' U' R U2 R' U' R U R'
(3,10,8,6)(4,5)         => R U2 R' U R U' R' U' R U' R' U'
(3,6,8,10)(4,7,5,9)     => U R U' R' U'
(3,6,8,10)(4,7)         => U R U R' U2 R U R'
(3,6,8,10)(4,7,9,5)     => R U' R' U R U2 R' U R U R2 U' R U' R' U2 R2 U R' U R U2 R' U
(3,6,8,10)(7,9)         => R U' R' U R U2 R' U R U R' U' R U2 R' U' R U' R'
(3,6,8,10)(5,9)         => U R U' R' U R' U U R U R' U R U' R U2 R' U' R U' R' U'
(3,6,8,10)(5,7)         => R U R' U R U2 R' U R U' R' U' R U2 R'
(3,6,8,10)(4,5)         => U R U R' U R U R' U' R U2 R'
(3,6,8,10)(4,5,9,7)     => U R U' R' U2 R' U' R U' R' U2 R U'
(3,6,8,10)(4,5,7,9)     => R U' R' U R U2 R' U R U2 U R' U' R U' R' U'
(3,6,8,10)(4,9)         => U R' U2 R U R' U R U2 R U' R' U'
(3,6,8,10)(4,9,7,5)     => U R U R' U R U2 R' U2 R' U2 R U R' U R U R U' R' U' R U' R'
(3,6,8,10)(4,9,5,7)     => U' R U2 R' U' R U' R' U R U' R' U' R U2 R' U' R U R' U'
(2,5,9)                 => R U R' U R U2 R' U R U' R' U2 R U2 R'
(2,5)(7,9)              => U' R U2 R' U' R U' R' U2 U' R U' R' U2 R U' R' U' R U R'
(2,5,7)                 => R U R' U R U2 R' U2
(2,5,9,7,4)             => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R2 U' R' U2 R U' R' U' R U R'
(2,5,4)                 => U R U R' U R U2 R' U
(2,5,7,9,4)             => U' R U2 R' U' R U' R' U' R' U' R U' R' U2 R U' U' R U' R' U2 R U' U' R' U'
(2,5,9,4,7)             => U R U' R' U R U R' U2 R U R2 U' R U' R' U2 R U'
(2,5,4,7,9)             => U R U R' U R U R' U2 R U2 R'
(2,5)(4,7)              => U' R U2 R' U' R U' R2 U2 R U R' U R U
(2,5,7,4,9)             => U' R U2 R' U' R U' R2 U2 R U R' U R2 U' R' U2 R U2 R'
(2,5)(4,9)              => U' R U2 R' U' R U' R' U' R U' R' U2 R U2 R' U'
(2,5,4,9,7)             => U R U2 R' U2 R U R' U2 R' U2 R U R' U R
(2,5,7)(3,8)(6,10)      => R U R' U2 R U R' U U2 R U R' U R U2 R' U
(2,5)(3,8)(6,10)(7,9)   => R' U' R U' R' U2 R U R U R'
(2,5,9)(3,8)(6,10)      => U' R U R' U U R' U U R U R' U R
(2,5)(3,8)(4,9)(6,10)   => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U' U2 R U' R' U2 R U' R' U' R U' R' U'
(2,5,7,4,9)(3,8)(6,10)  => U R U R' U R U R' U2 R U R2 U' R U' R' U2 R U'
(2,5,4,9,7)(3,8)(6,10)  => U R U R' U R U2 R' U R U R' U R U2 R' U R U R'
(2,5,9,7,4)(3,8)(6,10)  => U2 U R U R' U R U R' U R U2 R' U
(2,5,7,9,4)(3,8)(6,10)  => R U' R' U2 R U R' U R U2 R' U
(2,5,4)(3,8)(6,10)      => R U R' U2 R U R' U R' U' R U' R' U2 R2 U R' U R U2 R' U
(2,5)(3,8)(4,7)(6,10)   => R' U' R U' R' U2 R R U' R' U2 R U' R'
(2,5,9,4,7)(3,8)(6,10)  => U' R U2 R' U' R U' R' U' U' R U' R' U' U' R U' R' U' R U' R' U'
(2,5,4,7,9)(3,8)(6,10)  => R U' R2 U' R U' R' U2 R2 U R' U R U2 R' U
(2,5,9,7)(3,10,8,6)     => R' U' R U' R' U2 R U' U2 R U' R' U' R U2 R' U' R U R'
(2,5,7,9)(3,10,8,6)     => R U R' U R U R' U' R' U' R U' R' U2 R U'
(2,5)(3,10,8,6)         => R U2 R' U R U R' U
(2,5,9)(3,10,8,6)(4,7)  => U' R U2 R' U' R U' R' U R U' R'
(2,5,4,7)(3,10,8,6)     => R U R' U R U' U' R' U2 R U' R' U2 R U' R' U'
(2,5)(3,10,8,6)(4,7,9)  => R U R' U R U R' U U R' U U R U R' U R U R U R' U R U2 R' U
(2,5,9,4)(3,10,8,6)     => R' U' R U' R' U2 R2 U' R' U' R U' U' R' U' R U' R' U'
(2,5,4)(3,10,8,6)(7,9)  => R U R' U R U R' U U R U2 R' U' R U' R'
(2,5,7,4)(3,10,8,6)     => U R U R' U R U2 R' U R U' R' U2 R U' R' U'
(2,5,7)(3,10,8,6)(4,9)  => U R U2 R' U R U2 R' U
(2,5)(3,10,8,6)(4,9,7)  => U R U R' U R' U2 R U R' U R
(2,5,4,9)(3,10,8,6)     => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R2 U' R'
(2,5,7,4)(3,6,8,10)     => U R' U2 R U R' U R2 U' R' U' R U2 R'
(2,5,4)(3,6,8,10)(7,9)  => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U' U' R U' R' U' R U' R'
(2,5,9,4)(3,6,8,10)     => U R U' R' U R' U U R U R' U R
(2,5,7)(3,6,8,10)(4,9)  => U R U R' U R U2 R' U R U R' U R U2 R' U' R U' R' U'
(2,5)(3,6,8,10)(4,9,7)  => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U' U' R U' R' U' R U' R'
(2,5,4,9)(3,6,8,10)     => R U R' U R U R' U' R U R'
(2,5,7,9)(3,6,8,10)     => R U' R' U R U2 R' U R U R' U
(2,5)(3,6,8,10)         => U' R U' R' U' R U2 R'
(2,5,9,7)(3,6,8,10)     => U' R U2 R' U' R U' R' U' R U' R' U' R U' R'
(2,5,9)(3,6,8,10)(4,7)  => U2 R U2 R' U
(2,5)(3,6,8,10)(4,7,9)  => R' U' R U' R' U' U' R U' R U' R' U'
(2,5,4,7)(3,6,8,10)     => U R U R' U U R U R' U R U R' U R U2 R' U
(2,9,7)(3,8)(6,10)      => R U R' U R U2 R' U R U R'
(2,9,5)(3,8)(6,10)      => R' U' R U' R' U2 R U2 R U' R' U
(2,9)(3,8)(5,7)(6,10)   => R' U' R U' R' U2 R U2 R U' R' U' R U' U' R' U' R U' R'
(2,9,4)(3,8)(6,10)      => R U R' U R U U R' U R U R' U2 R U2 R' U' R U' R' U R U R' U R U2 R' U
(2,9,7,5,4)(3,8)(6,10)  => U R U R' U R U' R'
(2,9,5,7,4)(3,8)(6,10)  => U R U R' U R U2 R' U2 R' U2 R U R' U R U R U' R' U
(2,9)(3,8)(4,7)(6,10)   => U R U R' U R U2 R' U2 R' U2 R U R' U R U R U' R' U' R U' U' R' U' R U' R'
(2,9,5,4,7)(3,8)(6,10)  => R U R' U R U U R' U R U R' U' R' U' R U' R' U2 R U'
(2,9,4,7,5)(3,8)(6,10)  => U R' U2 R U R' U R2 U' R' U' U' R U' R' U' R U' R' U'
(2,9,7,4,5)(3,8)(6,10)  => U' R U2 R' U' R U' R2 U2 R U R' U R2 U R'
(2,9,4,5,7)(3,8)(6,10)  => U' R U' R' U' U' R U' R' U' R U' R' U'
(2,9)(3,8)(4,5)(6,10)   => U R U R' U R U2 R' U R U R' U R U2 R' U2 R U' R' U' R U' U' R' U' R U' R'
(2,9,5,7)(3,10,8,6)     => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U' R U R' U'
(2,9,7,5)(3,10,8,6)     => U' R U' R' U' R U2 R' U' R U R'
(2,9)(3,10,8,6)         => U R U R' U R U2 R' U R' U' R U' R' U2 R2 U' R'
(2,9)(3,10,8,6)(4,5,7)  => U2 R U' R'
(2,9,4,5)(3,10,8,6)     => R U' R' U R U' R' U' R U' R'
(2,9,7)(3,10,8,6)(4,5)  => R U' R' U R U R' U R' U' R U' R' U2 R U'
(2,9,4)(3,10,8,6)(5,7)  => U2 R U' R' U' R U' U' R' U' R U' R' U'
(2,9,7,4)(3,10,8,6)     => U R' U2 R U R' U R2 U' R' U' R U2 R' U' R U R'
(2,9,5,4)(3,10,8,6)     => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U' R U R' U'
(2,9,4,7)(3,10,8,6)     => R U' R' U R U R' U2
(2,9,5)(3,10,8,6)(4,7)  => U' R U2 R' U2
(2,9)(3,10,8,6)(4,7,5)  => U R' U2 R U R' U R U' R U' R'
(2,9,5)                 => R U2 R' U2 R U R' U' R U2 R' U' R U' R'
(2,9)(5,7)              => R' U' R U' R' U2 R U2 U' R U' R' U2 R U2 R'
(2,9,7)                 => R U2 R' U2 R U R' U
(2,9,4,5,7)             => R U R' U R U' U' R' U2 R U' R' U2 R U2 R' U'
(2,9,7,4,5)             => R U2 R' U2 R U' R' U' R U' R' U'
(2,9)(4,5)              => U R U R' U R U2 R' U R U R' U R U2 R' U R U' R' U2 R U2 R'
(2,9)(4,7)              => U R U R' U R U2 R' U2 R' U2 R U R' U R2 U' R' U2 R U2 R'
(2,9,4,7,5)             => R U2 R' U2 R U R2 U' R U' R' U2 R2 U R' U R U2 R' U
(2,9,5,4,7)             => R U2 R' U2 R U R2 U' R U' R' U2 R U'
(2,9,5,7,4)             => U' R U2 R' U' R U' R2 U2 R U R' U R2 U' R' U2 R U' R' U' R U R' U'
(2,9,4)                 => U R U R' U R U2 R' U R U' R' U2 R U2 R' U'
(2,9,7,5,4)             => R U U R' U2 R U R' U2 R U R' U R U2 R' U
(2,9,4)(3,6,8,10)(5,7)  => U R U R' U R U2 R' U2 R U' R' U'
(2,9,5,4)(3,6,8,10)     => R U R2 U2 R U R' U R
(2,9,7,4)(3,6,8,10)     => R U' R' U' R U' R' U' R U2 R' U' R U' R' U'
(2,9)(3,6,8,10)         => R U R2 U2 R U R' U R U' R U2 R' U' R U' R' U'
(2,9,5,7)(3,6,8,10)     => R U R' U R' U' R U' R' U2 R2 U R' U R U2 R' U
(2,9,7,5)(3,6,8,10)     => U R' U2 R U R' U R U R U' R' U' R U' R'
(2,9,7)(3,6,8,10)(4,5)  => R U' R' U' R U' R'
(2,9)(3,6,8,10)(4,5,7)  => R U R' U R' U' R U' R' U2 R U'
(2,9,4,5)(3,6,8,10)     => R U R2 U U R U R' U R U R U R' U R U2 R' U
(2,9,4,7)(3,6,8,10)     => R U R' U R U2 R' U' R U' R' U'
(2,9,5)(3,6,8,10)(4,7)  => R U R' U' R U R' U R U2 R' U
(2,9)(3,6,8,10)(4,7,5)  => R U R' U2
(2,7)(3,8)(5,9)(6,10)   => R U R' U R U2 R' U2 R U' R' U
(2,7,5)(3,8)(6,10)      => U' R U2 R' U' R U' R' U2 U' R U' R' U2 R U' R'
(2,7,9)(3,8)(6,10)      => R U' R' U' R U' U' R' U' R U' R'
(2,7,4)(3,8)(6,10)      => R U R' U2 R U' R' U' R U' R'
(2,7,9,5,4)(3,8)(6,10)  => U R U R' U R U2 R' U R U' R' U
(2,7,5,9,4)(3,8)(6,10)  => U' R U R' U2 R U2 R' U' R U' R' U R U R' U R U2 R' U
(2,7,4,5,9)(3,8)(6,10)  => U R' U2 R U R' U R U R U' R' U' R U' U' R' U' R U' R'
(2,7)(3,8)(4,5)(6,10)   => U' R U2 R' U' R U' R' U' R U R' U R U R' U2 R U' R'
(2,7,9,4,5)(3,8)(6,10)  => R U R' U R U2 R' U R U' R' U' U' R U' R' U' R U' R' U'
(2,7,4,9,5)(3,8)(6,10)  => U' R U2 R' U' R U' R2 U2 R U R' U R U R U' R' U
(2,7)(3,8)(4,9)(6,10)   => U R U R' U R U R' U' U' R U' R' U' R U' R' U'
(2,7,5,4,9)(3,8)(6,10)  => U R U R' U R U R' U U R U R' U
(2,7)(3,10,8,6)         => R U2 R' U R U R' U2 U R' U2 R U R' U R
(2,7,9,5)(3,10,8,6)     => R U R' U R U R' U R U R' U R U2 R' U
(2,7,5,9)(3,10,8,6)     => U' R U2 R' U' R U' R2 U2 R U R' U R U' R U' R'
(2,7,4)(3,10,8,6)(5,9)  => U R U R' U R U2 R' U2 R U R' U'
(2,7,5,4)(3,10,8,6)     => U' R U2 R' U' R U' R' U' R' U' R U' R' U2 R U' U' R U' R' U2 R U' R' U'
(2,7,9,4)(3,10,8,6)     => R U R' U R U R' U' R U2 R' U' R U' R' U'
(2,7,4,9)(3,10,8,6)     => U R U R' U R U2 R' U' R U' R'
(2,7)(3,10,8,6)(4,9,5)  => R U R' U R U2 R' U' R U R' U'
(2,7,5)(3,10,8,6)(4,9)  => U R U R' U R U2 R' U' R U' R' U' R U2 R' U' R U' R' U'
(2,7)(3,10,8,6)(4,5,9)  => U R U' R' U R U2 R' U R U R' U R' U' R U' R' U2 R U'
(2,7,4,5)(3,10,8,6)     => U' R U2 R' U' R U' R' U' R U' R' U' U' R U' R' U'
(2,7,9)(3,10,8,6)(4,5)  => R U R' U R U R'
(2,7,9)                 => U' R U' R' U2 R U2 R'
(2,7,5)                 => R' U' R U' R' U2 R U2
(2,7)(5,9)              => U' R U' R' U' U' R U' R' U' R U R' U'
(2,7,4)                 => U R U R' U R U2 R' U2 R' U2 R U R' U R U
(2,7,5,9,4)             => U R U' R' U R U R' U U R U R' U U R U R' U R U2 R' U
(2,7,9,5,4)             => R U' R' U R U R' U2 R U' R' U' R U' R'
(2,7)(4,9)              => U R U R' U R U2 R' U R U R' U R U2 R' U2 R U' R' U2 R U2 R' U'
(2,7,5,4,9)             => U R U U R' U2 R U R' U2 R U2 R' U' R U' R'
(2,7,4,9,5)             => U R' U2 R U R' U R2 U' R' U2 R U' R' U' R U R' U'
(2,7,4,5,9)             => U R' U2 R U R' U R2 U' R' U2 R U2 R'
(2,7,9,4,5)             => R' U' R U' R' U2 R U' U' R U' R' U2 R U' U' R' U'
(2,7)(4,5)              => U R U R' U R U2 R' U R U R' U R U2 R' U2
(2,7,9,4)(3,6,8,10)     => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U' R U' R' U'
(2,7,4)(3,6,8,10)(5,9)  => U2 R U' R' U' R U2 R' U' R U R' U'
(2,7,5,4)(3,6,8,10)     => U R U R' U R U2 R' U R U R' U R U2 R' U R U' R' U' R U2 R'
(2,7,9)(3,6,8,10)(4,5)  => U R' U2 R U R' U R U' R U' R' U' R U R'
(2,7)(3,6,8,10)(4,5,9)  => U R U' R' U R U2 R' U' R U' R'
(2,7,4,5)(3,6,8,10)     => U R U R' U U R U R' U U R U2 R' U' R U' R'
(2,7,5)(3,6,8,10)(4,9)  => U' R U2 R' U' R U2 R' U'
(2,7,4,9)(3,6,8,10)     => U2 R U' R' U' R U R'
(2,7)(3,6,8,10)(4,9,5)  => U R' U2 R U R' U R U' R U' R' U' R U2 R' U' R U R' U'
(2,7,9,5)(3,6,8,10)     => R U' R' U R U2 R' U R U R' U2 U R' U2 R U R' U R
(2,7)(3,6,8,10)         => R' U' R U' R' U2 R U' U2 R U' R' U' R U2 R'
(2,7,5,9)(3,6,8,10)     => U R U' R' U R U2 R' U' R U' R' U R U R' U R U2 R' U
(2,4,7,9,5)             => R U' R' U R U R' U2 R U R' R' U2 R U R' U R U R U R' U R U2 R' U
(2,4,7)                 => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U2
(2,4,7,5,9)             => U' R U2 R' U' R U' R' U' R' U' R U' R' U2 R U2 U' R U' R' U2 R U2 R'
(2,4,5)                 => U' R U2 R' U' R U' R' U'
(2,4,5,7,9)             => U' R U2 R' U' R U' R' U' U' R U' R' U' U' R U2 R'
(2,4,5,9,7)             => R U R' U R U R' U2 R U' R' U' R U R'
(2,4,9,7,5)             => U' R U2 R' U' R U' R2 U2 R U R' U R U' R U' R' U' U' R U' R' U' R U R'
(2,4,9,5,7)             => U' R U2 R' U' R U' R' U' U' R U' R' U' U' R U' R' U' R U R' U'
(2,4,9)                 => U R U2 R' U2 R U R' U' R U2 R' U' R U' R' U'
(2,4)(7,9)              => U R U R' U R U2 R' U' R U' R' U' U' R U' R' U' R U R'
(2,4)(5,9)              => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U R U' R' U2 R U' R' U' R U R' U'
(2,4)(5,7)              => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U2
(2,4,7,5)(3,6,8,10)     => U R U R' U2 R U R' U' R U2 R' U' R U' R' U'
(2,4,7)(3,6,8,10)(5,9)  => U R U' R' U2 R U2 R' U' R U' R' U'
(2,4,7,9)(3,6,8,10)     => R U' R' U R U2 R' U R U R2 U' R U' R' U2 R U'
(2,4,9,5)(3,6,8,10)     => U R U R' U R U U R' U R U R2 U2 R U R' U R
(2,4,9)(3,6,8,10)(5,7)  => U R U R' U R U U R' U R U R' U2
(2,4,9,7)(3,6,8,10)     => U R U R' U R U2 R' U R U' R' U' R U' R'
(2,4,5)(3,6,8,10)(7,9)  => R U R' U R U2 R' U' U' R U' R' U' R U' R'
(2,4,5,7)(3,6,8,10)     => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U R U' R' U' R U2 R'
(2,4,5,9)(3,6,8,10)     => U R U' R' U R' U U R U R' U R U R U R' U R U2 R' U
(2,4)(3,6,8,10)         => U' R U2 R' U' R U' R' U' U' R U' R' U' R U2 R'
(2,4)(3,6,8,10)(5,9,7)  => U' R U2 R' U' R U' R2 U2 R U R' U R U R U' R' U' R U' R'
(2,4)(3,6,8,10)(5,7,9)  => R' U' R U' R' U2 R2 U' R' U' R U2 R' U' R U R' U'
(2,4,7,9)(3,10,8,6)     => U R U R' U R U2 R' U R U R' U R U R'
(2,4,7)(3,10,8,6)(5,9)  => U R U' R' U R U2 R' U R U R' U2
(2,4,7,5)(3,10,8,6)     => R U2 R' U R U R2 U' R U' R' U2 R U'
(2,4)(3,10,8,6)(5,9,7)  => U R U' R' U R U2 R' U R U R2 U2 R U R' U R
(2,4)(3,10,8,6)         => R U2 R' U R U R' U U R U R' U R U2 R' U
(2,4)(3,10,8,6)(5,7,9)  => U R U R' U R U2 R' U2 R' U2 R U R' U R U2 R U R' U'
(2,4,9,5)(3,10,8,6)     => R' U' R U' R' U' U' R U' R U R' U'
(2,4,9,7)(3,10,8,6)     => U R U R' U R' U U R U R' U R U R U R' U R U2 R' U
(2,4,9)(3,10,8,6)(5,7)  => U R U R' U2 R U2 R' U' R U' R' U'
(2,4,5,9)(3,10,8,6)     => R' U' R U' R' U2 R2 U' R'
(2,4,5)(3,10,8,6)(7,9)  => R U R' U R U R' U U R U2 R' U' R U' R' U R U R' U R U2 R' U
(2,4,5,7)(3,10,8,6)     => R U2 R' U R U R' U' R U2 R' U' R U' R' U' R U2 R' U' R U' R' U'
(2,4,5,9,7)(3,8)(6,10)  => U' R U R' U' R U2 R' U' R U' R' U'
(2,4,5,7,9)(3,8)(6,10)  => R U R' U' R U' R' U'
(2,4,5)(3,8)(6,10)      => U' R U2 R' U' R U' R2 U2 R U R' U R U' R U' R' U2 R U' R'
(2,4,7,9,5)(3,8)(6,10)  => U' R U2 R' U' R U' R' U' R U' R' U
(2,4,7,5,9)(3,8)(6,10)  => U' R U R' U' R' U' R U' R' U2 R U2 R U2 R' U' R U' R' U'
(2,4,7)(3,8)(6,10)      => R U R' U R U R' U2 R U' R'
(2,4)(3,8)(5,7)(6,10)   => U R U R' U R U2 R' U' R U' R' U2 R U' R'
(2,4)(3,8)(5,9)(6,10)   => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U' U' R U' R' U
(2,4)(3,8)(6,10)(7,9)   => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U R U R'
(2,4,9,7,5)(3,8)(6,10)  => U' R U2 R' U' R U' R' U2 R U R'
(2,4,9)(3,8)(6,10)      => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U2 R U' R' U' R U' U' R' U' R U' R'
(2,4,9,5,7)(3,8)(6,10)  => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U2 R U' R' U
(1,6,8,3)(2,4,7,5)      => U'
(1,6,8,3)(2,4,7,9)      => U R' U2 R U R' U R U' R U' R' U2 R U2 R'
(1,6,8,3)(2,4,7)(5,9)   => U R' U2 R U R' U R U' R U' R' U' U' R U' R' U' R U R' U'
(1,6,8,3)(2,4,5)(7,9)   => R U' R' U R U R' U U R U R' U U2 R' U2 R U R' U R
(1,6,8,3)(2,4,5,9)      => U R U' R' U R U R' U2 R U R' U' R' U' R U' R' U2 R U'
(1,6,8,3)(2,4,5,7)      => U R U2 R' U' R U' R'
(1,6,8,3)(2,4,9,5)      => U R U U R' U2 R U R' U R' U2 R U R' U R
(1,6,8,3)(2,4,9)(5,7)   => U2 R U' R' U2 R U2 R'
(1,6,8,3)(2,4,9,7)      => U R U2 R' U2 R U R' U R U2 R' U' R U' R'
(1,6,8,3)(2,4)          => U R' U2 R U R' U R
(1,6,8,3)(2,4)(5,9,7)   => U R U R' U R U2 R' U R U R' U R U2 R' U' R U' R' U' U' R U' R' U' R U R'
(1,6,8,3)(2,4)(5,7,9)   => R U' R' U R U R' U U R U R' U
(1,6,10,8)(2,4,7)(5,9)  => U' R U R' U'
(1,6,10,8)(2,4,7,9)     => R U' R'
(1,6,10,8)(2,4,7,5)     => R U R' U2 R U R' U' R U2 R' U' R U' R'
(1,6,10,8)(2,4,5,9)     => U R' U2 R U R' U R U R U' R'
(1,6,10,8)(2,4,5)(7,9)  => R U' R' U2 R U2 R' U' R U' R'
(1,6,10,8)(2,4,5,7)     => U2 R U' R' U2 R U' R' U'
(1,6,10,8)(2,4)(5,9,7)  => U' R U R' U R' U2 R U R' U R
(1,6,10,8)(2,4)(5,7,9)  => R U' R' U2 R' U2 R U R' U R
(1,6,10,8)(2,4)         => R U R' U2 R U R' U
(1,6,10,8)(2,4,9,5)     => U R' U2 R U R' U R2 U R' U'
(1,6,10,8)(2,4,9,7)     => U R U R' U R U R' U2 R U R' U' R' U' R U' R' U2 R U'
(1,6,10,8)(2,4,9)(5,7)  => U R U R' U R U2 R' U R' U' R U' R' U2 R U2 R U' R'
(1,6)(2,4,7,9,5)(3,10)  => R U R' U R U2 R' U R U' R' U' R U2 R' U' R U R' U'
(1,6)(2,4,7)(3,10)      => R U2 R' U R U R' U' R U2 R' U' R U' R' U'
(1,6)(2,4,7,5,9)(3,10)  => R U R' U R U2 R' U R U' R' U' R U R'
(1,6)(2,4,5,9,7)(3,10)  => U R U R' U R U2 R' U R' U' R U' R' U2 R U' R U' R' U' R U' R'
(1,6)(2,4,5,7,9)(3,10)  => R U R' U R U2 R' U R U2 R' U
(1,6)(2,4,5)(3,10)      => R' U' R U' R' U2 R U2 R U' R' U' R U2 R'
(1,6)(2,4,9,7,5)(3,10)  => U R U' R' U' R U' R'
(1,6)(2,4,9,5,7)(3,10)  => U R U R2 U2 R U R' U R
(1,6)(2,4,9)(3,10)      => U R U R' U2
(1,6)(2,4)(3,10)(7,9)   => U R' U2 R U R' U R U' U' R U' R' U' R U' R'
(1,6)(2,4)(3,10)(5,9)   => U' R U2 R' U' R U' R2 U2 R U R' U R2 U' R' U' R U2 R' U' R U R' U'
(1,6)(2,4)(3,10)(5,7)   => U R U R' U R U2 R' U2 R' U2 R U R' U R U R U' R' U' R U2 R'
(1,6,3,8,10)(2,4,5,9,7) => U R U' R' U2
(1,6,3,8,10)(2,4,5)     => U R U R' U2 R U R' U'
(1,6,3,8,10)(2,4,5,7,9) => U R' U2 R U R' U R U R U' R' U' U' R U' R' U' R U' R'
(1,6,3,8,10)(2,4,7,9,5) => R U' R' U R U2 R' U R U R' U' R U2 R' U' R U' R' U'
(1,6,3,8,10)(2,4,7,5,9) => U R U' R2 U2 R U R' U R
(1,6,3,8,10)(2,4,7)     => R U R' U R U2 R' U R U' R' U' R U2 R' U'
(1,6,3,8,10)(2,4)(5,7)  => U R U R' U R U R' U' R U2 R' U'
(1,6,3,8,10)(2,4)(5,9)  => U R U R' U' R U' R'
(1,6,3,8,10)(2,4)(7,9)  => U R U R' U R U2 R' U R' U' R U' R' U' U' R U' R U' R' U2
(1,6,3,8,10)(2,4,9,7,5) => U R' U2 R U R' U R U2 R U' R' U2
(1,6,3,8,10)(2,4,9,5,7) => U R U R' U R U2 R' U2 R' U2 R U R' U R U R U' R' U' R U' R' U'
(1,6,3,8,10)(2,4,9)     => R U' R' U' U' R U' R' U' R U' R'
(1,6,8,3)(4,7,5,9)      => R U R' U R U2 R' U R U' R' U2 R U2 R' U'
(1,6,8,3)(4,7,9,5)      => U' R U2 R' U' R U' R' U2 U' R U' R' U2 R U' R' U' R U R' U'
(1,6,8,3)(4,7)          => R U R' U R U2 R' U
(1,6,8,3)(5,9)          => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R2 U' R' U2 R U' R' U' R U R' U'
(1,6,8,3)(5,7)          => U R U R' U R U2 R'
(1,6,8,3)(7,9)          => U' R U2 R' U' R U' R2 U2 R U R' U R U2 R U' R' U2 R U' R' U' R U R'
(1,6,8,3)(4,5,9,7)      => U R U R' U R U2 R' U2 R U' R' U2 R U' R' U' R U R'
(1,6,8,3)(4,5,7,9)      => U R U R' U R U R' U2 R U2 R' U'
(1,6,8,3)(4,5)          => U' R U2 R' U' R U' R2 U2 R U R' U R
(1,6,8,3)(4,9)          => U' R U2 R' U' R U' R2 U2 R U R' U R2 U' R' U2 R U2 R' U'
(1,6,8,3)(4,9,7,5)      => R U R' U R U2 R' U' R U' R' U' U' R U' R' U' R U R'
(1,6,8,3)(4,9,5,7)      => U R U2 R' U U R U2 R' U R U2 R' U
(1,6,10,8)(4,7)         => U R U R' U R U2 R' U R U R' U R U R' U2 R U' R' U'
(1,6,10,8)(4,7,9,5)     => R U' R' U R U R' U R U2 R' U
(1,6,10,8)(4,7,5,9)     => U' R U2 R' U R U2 R' U
(1,6,10,8)(4,9,7,5)     => U' R U2 R' U' R U' R' U' R U R' U R U' U' R' U' R U' R' U' R U2 R' U' R U R'
(1,6,10,8)(4,9)         => U R U R' U R U R' U U R U R' U U R U2 R' U' R U' R'
(1,6,10,8)(4,9,5,7)     => U R U R' U R U2 R' U R U R' U R U2 R' U R U R' U'
(1,6,10,8)(5,9)         => U R U R' U R U2 R' U2 R' U2 R U R' U R2 U R' U'
(1,6,10,8)(7,9)         => U' R U2 R' U' R U2 R' U' R U2 R' U' R U R'
(1,6,10,8)(5,7)         => U R U R' U R U2 R' U2 R' U2 R U R' U R U' R U' R' U' U' R U' R' U'
(1,6,10,8)(4,5)         => R' U' R U' R' U2 R R U' R' U2 R U' R' U'
(1,6,10,8)(4,5,9,7)     => U' R U R' U R' U U R U R' U R U R U R' U R U2 R' U
(1,6,10,8)(4,5,7,9)     => U R U R' U R U2 R' U R U' R' U' R U' U' R' U' R U' R' U'
(1,6)(3,10)(4,7)(5,9)   => R' U' R U' R' U2 R U' U2 R U' R' U' R U2 R' U' R U R' U'
(1,6)(3,10)(4,7,9)      => R U R' U R U R' U R U2 R' U' R U' R'
(1,6)(3,10)(4,7,5)      => R U2 R' U R U R'
(1,6)(3,10)(4,5,9)      => U' R U2 R' U' R U' R' U R U' R' U'
(1,6)(3,10)(4,5,7)      => R U' R' U' R U2 R'
(1,6)(3,10)(4,5)(7,9)   => U' R U2 R' U' R U' R2 U2 R U R' U R U' U' R U' R' U' R U' R'
(1,6)(3,10)(5,9,7)      => U R U R' U R U2 R' U2 R U' R' U' R U' R'
(1,6)(3,10)(5,7,9)      => R U R' U R U R' U2 R U2 R' U' R U' R' U'
(1,6)(3,10)             => U R U R' U R U2 R' U R' U' R U' R' U2 R U2 R U' R' U' R U2 R'
(1,6)(3,10)(4,9,7)      => R U R' U R U' U' R' U' R U' R' U' R U' R'
(1,6)(3,10)(4,9,5)      => U R U R' U' R U R' U R U2 R' U
(1,6)(3,10)(4,9)(5,7)   => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R2 U' R' U'
(1,6,3,8,10)            => U R U R' U2 R U2 R' U R U2 R' U
(1,6,3,8,10)(5,7,9)     => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U' U' R U' R' U' R U' R' U'
(1,6,3,8,10)(5,9,7)     => U R U' R' U' R U R' U R U2 R' U
(1,6,3,8,10)(4,9,7)     => U R U R' U R U2 R' U R U R' U R U2 R' U' R U' R' U2
(1,6,3,8,10)(4,9,5)     => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U' U' R U' R' U' R U' R' U'
(1,6,3,8,10)(4,9)(5,7)  => R U R' U R U R' U' R U R' U'
(1,6,3,8,10)(4,7,9)     => R U' R' U R U2 R' U R U R'
(1,6,3,8,10)(4,7,5)     => U' R U' R' U' R U2 R' U'
(1,6,3,8,10)(4,7)(5,9)  => U' R U2 R' U' R U' R' U' R U' R' U' R U' R' U'
(1,6,3,8,10)(4,5,9)     => U R U R' U' R U' R' U R U R' U R U2 R' U
(1,6,3,8,10)(4,5)(7,9)  => R' U' R U' R' U' U' R U' R U' R' U2
(1,6,3,8,10)(4,5,7)     => U R U R' U U R U R' U R U2 R' U' R U' R' U R U R' U R U2 R' U
(1,6,10,8)(2,9,5)(4,7)  => R U R' U R U2 R' U R U R' U'
(1,6,10,8)(2,9)(4,7,5)  => R' U' R U' R' U2 R U2 R U' R'
(1,6,10,8)(2,9,4,7)     => R U R' U R U U R' U R U U R' U R U2 R' U
(1,6,10,8)(2,9,7,5)     => U R U R' U R U2 R' U R U R' U R U2 R' U' R U' R' U' R U2 R' U' R U R'
(1,6,10,8)(2,9,5,7)     => U R U R' U R U' R' U'
(1,6,10,8)(2,9)         => U R U R' U R U2 R' U2 R' U2 R U R' U R U R U' R'
(1,6,10,8)(2,9,4,5)     => R U R' U R U U R' U R U R' U2 R' U' R U' R' U2 R U'
(1,6,10,8)(2,9)(4,5,7)  => R U R' U R U U R' U R U R' U R U2 R' U' R U' R'
(1,6,10,8)(2,9,7)(4,5)  => R U R' U R U U R' U R U R' U R' U U R U R' U R U R U R' U R U2 R' U
(1,6,10,8)(2,9,5,4)     => U' R U2 R' U' R U' R2 U2 R U R' U R2 U R' U'
(1,6,10,8)(2,9,7,4)     => R' U' R U' R' U' U' R U' R U' R' U' R U2 R' U' R U R'
(1,6,10,8)(2,9,4)(5,7)  => R U R' U R U U R' U R U R' U R U2 R' U' R U' R' U' R U2 R' U' R U' R' U'
(1,6)(2,9)(3,10)(4,7)   => R' U' R U' R' U2 R U' U2 R U' R' U' R U R'
(1,6)(2,9,5,4,7)(3,10)  => U' R U' R' U' R U2 R' U' R U R' U'
(1,6)(2,9,4,7,5)(3,10)  => U R U R' U R U2 R' U R' U' R U' R' U2 R2 U' R' U'
(1,6)(2,9,4)(3,10)      => U2 R U' R' U'
(1,6)(2,9,7,5,4)(3,10)  => U' R U2 R' U' R U2 R' U' R U' R'
(1,6)(2,9,5,7,4)(3,10)  => R U' R' U R U R' U' R U2 R' U' R U' R'
(1,6)(2,9,7)(3,10)      => R U' R' U R U R' U U R U R' U R U2 R' U
(1,6)(2,9,5)(3,10)      => R U' R' U R U R2 U' R U' R' U2 R U'
(1,6)(2,9)(3,10)(5,7)   => U R U R' U R U2 R' U R U R' U R U2 R' U R U' R' U' R U R'
(1,6)(2,9,7,4,5)(3,10)  => R U' R' U R U R' U
(1,6)(2,9)(3,10)(4,5)   => U R U R' U R U2 R' U2 R' U2 R U R' U R2 U' R' U' R U R'
(1,6)(2,9,4,5,7)(3,10)  => U R' U2 R U R' U R U' R U' R' U'
(1,6,8,3)(2,9)(4,7,5)   => R U2 R' U2 R U R' U' R U2 R' U' R U' R' U'
(1,6,8,3)(2,9,4,7)      => R U2 R' U U R U R' U R U R' U R U2 R' U
(1,6,8,3)(2,9,5)(4,7)   => R U2 R' U2 R U R'
(1,6,8,3)(2,9,7,4)      => U' R U2 R' U' R U2 R' U2 R U' R' U' R U R'
(1,6,8,3)(2,9,5,4)      => R' U' R U' R' U2 R R U' R' U2 R U' R' U' R U R' U'
(1,6,8,3)(2,9,4)(5,7)   => U R U R' U R U2 R' U R U R' U R U2 R' U R U' R' U2 R U2 R' U'
(1,6,8,3)(2,9,4,5)      => R U2 R' U2 R U R' U' R' U' R U' R' U2 R U'
(1,6,8,3)(2,9,7)(4,5)   => R U2 R' U2 R U R' U2 R' U2 R U R' U R U R U R' U R U2 R' U
(1,6,8,3)(2,9)(4,5,7)   => R U U R' U2 R U R' U2 R U2 R' U' R U' R'
(1,6,8,3)(2,9)          => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R2 U' R' U2 R U2 R'
(1,6,8,3)(2,9,7,5)      => R U2 R' U2 R U R' U2 R' U2 R U R' U R U' R U2 R' U' R U' R' U'
(1,6,8,3)(2,9,5,7)      => R U U R' U2 R U R' U2 R U2 R' U' R U' R' U R U R' U R U2 R' U
(1,6,3,8,10)(2,9,7)     => R U R2 U' R U' R' U2 R U'
(1,6,3,8,10)(2,9)(5,7)  => R U R' U2 R U R' U R U2 R' U
(1,6,3,8,10)(2,9,5)     => R U R' U' R U2 R' U' R U' R' U' R U2 R' U' R U' R' U'
(1,6,3,8,10)(2,9,4,7,5) => R U R' U2 U R' U2 R U R' U R
(1,6,3,8,10)(2,9)(4,7)  => R U R' U' R' U U R U R' U R U R U R' U R U2 R' U
(1,6,3,8,10)(2,9,5,4,7) => U R' U2 R U R' U R U R U' R' U' R U' R' U'
(1,6,3,8,10)(2,9,5,7,4) => R U' R' U' R U' R' U'
(1,6,3,8,10)(2,9,4)     => R U R' U' R U2 R' U' R U' R'
(1,6,3,8,10)(2,9,7,5,4) => R U R2 U' R U' R' U2 R2 U R' U R U2 R' U
(1,6,3,8,10)(2,9,7,4,5) => R U R' U R U2 R' U' R U' R' U2
(1,6,3,8,10)(2,9)(4,5)  => U' R U2 R' U' R U' R' U' R U' R' U' U' R U' R' U' R U' R'
(1,6,3,8,10)(2,9,4,5,7) => R U R' U
(1,6,10,8)(2,5,9)(4,7)  => R U R' U R U2 R' U2 R U' R'
(1,6,10,8)(2,5,4,7)     => U' R U2 R' U' R U' R' U2 U' R U' R' U2 R U' R' U'
(1,6,10,8)(2,5)(4,7,9)  => R U' R' U' R U' U' R' U' R U' R' U'
(1,6,10,8)(2,5)         => R U R' U2 R U' R' U' R U' R' U'
(1,6,10,8)(2,5,7,9)     => U R U R' U R U2 R' U R U' R'
(1,6,10,8)(2,5,9,7)     => U R' U2 R U R' U R U2 R U' R' U' R U2 R' U' R U R'
(1,6,10,8)(2,5,9,4)     => U R' U2 R U R' U R U R U' R' U' R U' U' R' U' R U' R' U'
(1,6,10,8)(2,5,7,4)     => U' R U2 R' U' R U' R' U' R U R' U R U R' U2 R U' R' U'
(1,6,10,8)(2,5,4)(7,9)  => U R U' R' U' R U2 R' U' R U R'
(1,6,10,8)(2,5,4,9)     => U' R U2 R' U' R U' R2 U2 R U R' U R U R U' R'
(1,6,10,8)(2,5)(4,9,7)  => U R U R' U R U2 R' U R' U' R U' R' U' U' R U' R U' R' U' R U2 R' U' R U R'
(1,6,10,8)(2,5,7)(4,9)  => U R U R' U R U R' U2 R U R'
(1,6)(2,5)(3,10)(4,7)   => U' R U2 R' U' R U' R' U' R U' R' U' R U' U' R'
(1,6)(2,5,4,7,9)(3,10)  => U' R U' R' U' R U R'
(1,6)(2,5,9,4,7)(3,10)  => U' R U2 R' U' R U' R2 U2 R U R' U R U' R U' R' U'
(1,6)(2,5,9)(3,10)      => U R' U2 R U R' U R2 U' R' U' R U R'
(1,6)(2,5,7)(3,10)      => R U2 R' U R U R' U' R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,6)(2,5)(3,10)(7,9)   => U R U R' U R U2 R' U2 R' U2 R U R' U R U' U' R U' R' U' R U' R'
(1,6)(2,5)(3,10)(4,9)   => U R U R' U R U2 R' U' R U' R' U'
(1,6)(2,5,7,4,9)(3,10)  => U R U R2 U2 R U R' U R U' R U2 R' U' R U' R' U'
(1,6)(2,5,4,9,7)(3,10)  => R' U' R U' R' U2 R U' R U' R' U' R U' R'
(1,6)(2,5,9,7,4)(3,10)  => U R U' R' U R U2 R' U R U R' U' R U2 R' U' R U' R'
(1,6)(2,5,4)(3,10)      => R U2 R' U R U R' U U R' U U R U R' U R
(1,6)(2,5,7,9,4)(3,10)  => R U R' U R U R' U'
(1,6,8,3)(2,5)(4,7,9)   => U' R U' R' U2 R U2 R' U'
(1,6,8,3)(2,5,4,7)      => R' U' R U' R' U2 R U
(1,6,8,3)(2,5,9)(4,7)   => U R U' R' U R U R' U2 R U R'
(1,6,8,3)(2,5)          => U R U R' U R U2 R' U2 R' U2 R U R' U R
(1,6,8,3)(2,5,9,7)      => U R U R' U R U2 R' U R' U' R U' R' U2 R U' R U' R' U2 R U' R' U' R U R'
(1,6,8,3)(2,5,7,9)      => R U' R' U R U R' U2 R U' R' U' R U' R' U'
(1,6,8,3)(2,5)(4,9,7)   => U R U' R' U2 R U' R' U' R U R'
(1,6,8,3)(2,5,7)(4,9)   => U R U2 R' U2 R U R' U2 R U2 R' U' R U' R' U'
(1,6,8,3)(2,5,4,9)      => R' U' R U' R' U2 R R U' R' U2 R U2 R'
(1,6,8,3)(2,5,9,4)      => U R' U2 R U R' U R2 U' R' U2 R U2 R' U'
(1,6,8,3)(2,5,4)(7,9)   => U R' U2 R U R' U R U2 R U' R' U2 R U' R' U' R U R'
(1,6,8,3)(2,5,7,4)      => U R U R' U R U2 R' U R U R' U R U2 R' U
(1,6,3,8,10)(2,5)(7,9)  => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U' R U' R' U2
(1,6,3,8,10)(2,5,9)     => U R U R' U' R U' R' U' R U2 R' U' R U' R' U'
(1,6,3,8,10)(2,5,7)     => U R U R' U R U2 R' U R U R' U R U2 R' U R U' R' U' R U2 R' U'
(1,6,3,8,10)(2,5,7,9,4) => U R' U2 R U R' U R U' R U' R' U' R U R' U'
(1,6,3,8,10)(2,5,9,7,4) => U R U' R' U R U2 R' U' R U' R' U'
(1,6,3,8,10)(2,5,4)     => U R U R' U2 R U R' U2 R U2 R' U' R U' R' U'
(1,6,3,8,10)(2,5,4,9,7) => U' R U2 R' U' R U2 R' U2
(1,6,3,8,10)(2,5)(4,9)  => U2 R U' R' U' R U R' U'
(1,6,3,8,10)(2,5,7,4,9) => R U R' U R U' U' R' U2 R U' R' U2 R U' R' U' R U' R'
(1,6,3,8,10)(2,5,4,7,9) => R U' R' U R U U R' U R U R' U R U R' U R U2 R' U
(1,6,3,8,10)(2,5)(4,7)  => R' U' R U' R' U2 R U' U2 R U' R' U' R U2 R' U'
(1,6,3,8,10)(2,5,9,4,7) => U R U' R2 U2 R U R' U R U' R U2 R' U' R U' R' U'
(1,6,8,3)(2,7,9)(4,5)   => U' R U2 R' U' R U' R2 U2 R U R' U R U' R U' R' U2 R U2 R'
(1,6,8,3)(2,7,4,5)      => U2 R' U' R U' R' U2 R U'
(1,6,8,3)(2,7)(4,5,9)   => U' R U2 R' U' R U' R' U' R' U' R U' R' U2 R U2 U' R U' R' U2 R U2 R' U'
(1,6,8,3)(2,7,5,4)      => U' R U2 R' U' R U' R' U2
(1,6,8,3)(2,7,9,4)      => U' R U2 R' U' R U' R' U' U' R U' R' U' U' R U2 R' U'
(1,6,8,3)(2,7,4)(5,9)   => R U R' U R U R' U2 R U' R' U' R U R' U'
(1,6,8,3)(2,7)(4,9,5)   => U R U2 R' U2 R U R' U2 R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,6,8,3)(2,7,4,9)      => R U R' U R U R' U2 R U2 R'
(1,6,8,3)(2,7,5)(4,9)   => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U R U' R' U2 R U2 R' U'
(1,6,8,3)(2,7,9,5)      => U R U R' U R U2 R' U' R U' R' U' U' R U' R' U' R U R' U'
(1,6,8,3)(2,7,5,9)      => U R U R' U R U2 R' U' R U' R' U2 R U2 R'
(1,6,8,3)(2,7)          => U2 R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,6,3,8,10)(2,7)(4,5)  => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U R U' R' U' R U2 R' U'
(1,6,3,8,10)(2,7,4,5,9) => U R U' R' U R' U' R U' R' U2 R U2 R U2 R' U' R U' R' U'
(1,6,3,8,10)(2,7,9,4,5) => R U' R' U R U2 R' U R U R' U2 R U2 R' U' R U' R'
(1,6,3,8,10)(2,7,5,4,9) => R' U' R U' R' U2 R U' U' R U' R' U2 R U' R' U' R U' R'
(1,6,3,8,10)(2,7)(4,9)  => U R U R' U R U U R' U R U R' U
(1,6,3,8,10)(2,7,4,9,5) => U R U R' U R U2 R' U R U' R' U' R U' R' U'
(1,6,3,8,10)(2,7,9,5,4) => R U R' U R U2 R' U' U' R U' R' U' R U' R' U'
(1,6,3,8,10)(2,7,4)     => U R U R' U U R U R' U U R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,6,3,8,10)(2,7,5,9,4) => U R U' R' U R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,6,3,8,10)(2,7,5)     => U' R U2 R' U' R U' R' U' U' R U' R' U' R U2 R' U'
(1,6,3,8,10)(2,7)(5,9)  => U R U' R' U R' U' R U' R' U2 R U'
(1,6,3,8,10)(2,7,9)     => U R U R' U R U2 R' U2 R' U2 R U R' U R U R U' R' U' U' R U' R' U' R U' R'
(1,6)(2,7,9,4,5)(3,10)  => R U R' U R U R' U R' U2 R U R' U R
(1,6)(2,7,4,5,9)(3,10)  => U R U' R' U R U2 R' U R U R' U
(1,6)(2,7)(3,10)(4,5)   => R U R' U R U2 R' U2 R U' R' U' R U2 R'
(1,6)(2,7)(3,10)(5,9)   => U' R U2 R' U' R U' R' U' U' R U' R' U' R U2 R' U' R U R' U'
(1,6)(2,7,5)(3,10)      => U' R U2 R' U' R U' R2 U2 R U R' U R U R U' R' U' R U2 R'
(1,6)(2,7,9)(3,10)      => U' R U2 R' U' R U' R' U' U' R U' R' U' R U R'
(1,6)(2,7,5,4,9)(3,10)  => U R U R' U R' U' R U' R' U2 R U'
(1,6)(2,7,4,9,5)(3,10)  => U R U R' U R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,6)(2,7)(3,10)(4,9)   => U R U R' U R U2 R' U2 R' U2 R U R' U R U' R U' R' U'
(1,6)(2,7,5,9,4)(3,10)  => R' U' R U' R' U2 R2 U' R' U'
(1,6)(2,7,9,5,4)(3,10)  => R U R' U R U R' U R' U2 R U R' U R U' R U2 R' U' R U' R' U'
(1,6)(2,7,4)(3,10)      => U R U R' U R U2 R' U R U' R' U' R U2 R'
(1,6,10,8)(2,7,4)(5,9)  => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U R U R' U'
(1,6,10,8)(2,7,9,4)     => U' R U2 R' U' R U' R' U' R U' R' U' R U' U' R' U' R U' R' U'
(1,6,10,8)(2,7,5,4)     => R U R' U2 R U R2 U' R U' R' U2 R U'
(1,6,10,8)(2,7,9)(4,5)  => U' R U2 R' U' R U' R' U' R U' R'
(1,6,10,8)(2,7)(4,5,9)  => U' R U R' U2 R' U' R U' R' U2 R U'
(1,6,10,8)(2,7,4,5)     => R U R' U R U R' U2 R U' R' U'
(1,6,10,8)(2,7)         => U R U R' U R U2 R' U' R U' R' U' U' R U' R' U'
(1,6,10,8)(2,7,5,9)     => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U' U' R U' R'
(1,6,10,8)(2,7,9,5)     => R U' R' U' R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,6,10,8)(2,7)(4,9,5)  => U' R U2 R' U' R U' R' U2 R U R' U'
(1,6,10,8)(2,7,5)(4,9)  => U R U R' U R U R' U2 R U R' U U R' U2 R U R' U R
(1,6,10,8)(2,7,4,9)     => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U2 R U' R'
(1,8)(2,7)(3,6)(4,5)    => U2
(1,8)(2,7,9,4,5)(3,6)   => U R' U2 R U R' U R U' R U' R' U2 R U2 R' U'
(1,8)(2,7,4,5,9)(3,6)   => R' U' R U' R' U2 R U' R U' R' U2 R U2 R'
(1,8)(2,7,9,5,4)(3,6)   => R U' R' U R U R' U U R U R' U R U R' U R U2 R' U
(1,8)(2,7,5,9,4)(3,6)   => U R U' R' U R U R' U U R U R' U R U2 R' U' R U' R'
(1,8)(2,7,4)(3,6)       => U R U2 R' U' R U' R' U'
(1,8)(2,7,5,4,9)(3,6)   => U R U2 R' U2 R U R' U U2 R U R' U R U2 R' U
(1,8)(2,7)(3,6)(4,9)    => U2 R U' R' U2 R U2 R' U'
(1,8)(2,7,4,9,5)(3,6)   => U R U2 R' U2 R U R' U R U2 R' U' R U' R' U'
(1,8)(2,7,5)(3,6)       => U R' U2 R U R' U R U'
(1,8)(2,7)(3,6)(5,9)    => U R U R' U R U2 R' U R U R' U R U2 R' U' R U' R' U' U' R U' R' U' R U R' U'
(1,8)(2,7,9)(3,6)       => R U' R' U R U R' U2 R U R'
(1,8,6,10,3)(2,7,4,5,9) => U' R U R' U2
(1,8,6,10,3)(2,7,9,4,5) => R U' R' U'
(1,8,6,10,3)(2,7)(4,5)  => R U R' U2 R U R' U' R U2 R' U' R U' R' U'
(1,8,6,10,3)(2,7,5,9,4) => U R' U2 R U R' U R U R U' R' U'
(1,8,6,10,3)(2,7,9,5,4) => R U' R' U2 R U2 R' U' R U' R' U'
(1,8,6,10,3)(2,7,4)     => R U R' U U R U R' U R U R' U R U2 R' U
(1,8,6,10,3)(2,7)(5,9)  => U' R U R' U' R U R' U R U2 R' U
(1,8,6,10,3)(2,7,9)     => U R U2 R' U
(1,8,6,10,3)(2,7,5)     => R U R' U2 R U R'
(1,8,6,10,3)(2,7,5,4,9) => U R U R' U R U2 R' U2 R U' R' U' R U R'
(1,8,6,10,3)(2,7,4,9,5) => U R U R' U R U R' U U R U R' U R U2 R' U' R U' R'
(1,8,6,10,3)(2,7)(4,9)  => U R U R' U R U2 R' U R' U' R U' R' U2 R U2 R U' R' U'
(1,8,3,10)(2,7,9)(4,5)  => U R U R' U R U2 R' U2 R U' R' U' U' R U' R' U' R U' R'
(1,8,3,10)(2,7,4,5)     => U R U R' U R U2 R' U R U R' U R U2 R' U2 R U' R' U' R U2 R' U'
(1,8,3,10)(2,7)(4,5,9)  => R U R' U R U2 R' U R U' R' U' R U R' U'
(1,8,3,10)(2,7,4)(5,9)  => U R U R' U R U2 R' U R' U' R U' R' U2 R U' R U' R' U' R U' R' U'
(1,8,3,10)(2,7,9,4)     => U R U R' U R U R' U' R U R' U'
(1,8,3,10)(2,7,5,4)     => R' U' R U' R' U2 R U2 R U' R' U' R U2 R' U'
(1,8,3,10)(2,7)(4,9,5)  => U R U' R' U' R U' R' U'
(1,8,3,10)(2,7,4,9)     => U R U R' U U R U R' U R U2 R' U
(1,8,3,10)(2,7,5)(4,9)  => U R U R' U
(1,8,3,10)(2,7,9,5)     => R U R' U R U' R' U' R U' R'
(1,8,3,10)(2,7,5,9)     => R U R' U R U2 R' U' R U' R' U' U' R U' R' U' R U' R'
(1,8,3,10)(2,7)         => R U2 R' U R U R' U2 R' U' R U' R' U2 R U'
(1,8,10,6)(2,7,4)(5,9)  => U R U' R' U
(1,8,10,6)(2,7,5,4)     => U R U R' U U R U R' U U
(1,8,10,6)(2,7,9,4)     => U R' U2 R U R' U R U R U' R' U' U' R U' R' U' R U' R' U'
(1,8,10,6)(2,7,9)(4,5)  => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U' R U' R' U' R U' U' R' U' R U' R'
(1,8,10,6)(2,7)(4,5,9)  => U R U' R' U2 R U R' U R U2 R' U
(1,8,10,6)(2,7,4,5)     => U R U R' U2 R U R' U U2 R U R' U R U2 R' U
(1,8,10,6)(2,7)         => U R U R' U U R U R' U R U2 R' U' R U' R' U'
(1,8,10,6)(2,7,5,9)     => U R U R' U' R U' R' U'
(1,8,10,6)(2,7,9,5)     => R U' R' U R U2 R' U R U R' U2 R' U' R U' R' U2 R U'
(1,8,10,6)(2,7)(4,9,5)  => U R' U2 R U R' U R U2 R U' R' U
(1,8,10,6)(2,7,4,9)     => U' R U2 R' U' R U2 R' U' R U2 R' U' R U' R'
(1,8,10,6)(2,7,5)(4,9)  => R U' R' U' U' R U' R' U' R U' R' U'
(1,8)(2,4,5,9,7)(3,6)   => U' R U2 R' U' R U' R' U' R U' R' U' U' R U' R' U' R U R'
(1,8)(2,4,5,7,9)(3,6)   => R U R' U R U2 R' U' R U' R' U2 R U2 R'
(1,8)(2,4,5)(3,6)       => R U R' U R U2 R'
(1,8)(2,4,7,5,9)(3,6)   => U' R U2 R' U' R U' R2 U2 R U R' U R U2 R U' R' U2 R U2 R'
(1,8)(2,4,7)(3,6)       => U R U R' U R U2 R' U'
(1,8)(2,4,7,9,5)(3,6)   => R U' R' U R U R' U2 R U R' U' R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,8)(2,4)(3,6)(5,9)    => U R U R' U R U2 R' U2 R U' R' U2 R U' R' U' R U R' U'
(1,8)(2,4)(3,6)(7,9)    => U' R U2 R' U' R U' R' U' R U R' U R U' U' R' U2 R U' R' U2 R U' R' U' R U R'
(1,8)(2,4)(3,6)(5,7)    => U' R U2 R' U' R U' R2 U2 R U R' U R U'
(1,8)(2,4,9,7,5)(3,6)   => U R U2 R' U2 R U R' U R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,8)(2,4,9,5,7)(3,6)   => R U R' U R U2 R' U' R U' R' U' U' R U' R' U' R U R' U'
(1,8)(2,4,9)(3,6)       => U R U R' U R U2 R' U2 R U' R' U2 R U2 R'
(1,8,6,10,3)(2,4,5)     => U R' U2 R U R' U R U' R U' R' U' R U2 R'
(1,8,6,10,3)(2,4,5,7,9) => R U' R' U R U2 R' U' R U' R' U R U R' U R U2 R' U
(1,8,6,10,3)(2,4,5,9,7) => U' R U' R' U' R U' R' U R U R' U R U2 R' U
(1,8,6,10,3)(2,4,9,5,7) => U' R U2 R' U' R U' R' U' R U R' U R U' U' R' U' R U' R' U' R U2 R' U' R U R' U'
(1,8,6,10,3)(2,4,9,7,5) => U R U R' U R U R' U2 R U R' U2 R U2 R' U' R U' R' U'
(1,8,6,10,3)(2,4,9)     => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U' R U' R' U' R U R'
(1,8,6,10,3)(2,4,7,5,9) => U' R U2 R' U' R U2 R' U' R U2 U' R'
(1,8,6,10,3)(2,4,7,9,5) => U' R U2 R' U' R U2 R' U' R U2 R' U' R U R' U'
(1,8,6,10,3)(2,4,7)     => U2 R U' R' U' R U2 R'
(1,8,6,10,3)(2,4)(5,7)  => U R U R' U R U2 R' U R' U' R U' R' U2 R2 U' R' U' R U2 R'
(1,8,6,10,3)(2,4)(5,9)  => U' R U R' U R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,8,6,10,3)(2,4)(7,9)  => R' U' R U' R' U2 R U' U2 R U' R' U' R U' R'
(1,8,3,10)(2,4,5,9)     => U R U' R' U R U U R' U R U R' U R U R' U R U2 R' U
(1,8,3,10)(2,4,5)(7,9)  => R U R' U R U R' U R U2 R' U' R U' R' U'
(1,8,3,10)(2,4,5,7)     => R U2 R' U R U R' U'
(1,8,3,10)(2,4)(5,9,7)  => U' R U2 R' U' R U' R' U2 U' R U' R' U2
(1,8,3,10)(2,4)         => R U' R' U' R U2 R' U'
(1,8,3,10)(2,4)(5,7,9)  => R U R' U R U R2 U U R U R' U R U R U R' U R U2 R' U
(1,8,3,10)(2,4,7)(5,9)  => U R U R' U R U2 R' U2 R U' R' U' R U' R' U'
(1,8,3,10)(2,4,7,9)     => U' R U2 R' U' R U2 R' U' U' R U' R' U' R U' R'
(1,8,3,10)(2,4,7,5)     => R U2 R' U R U R' U R' U2 R U R' U R
(1,8,3,10)(2,4,9,5)     => R U R' U R U' U' R' U' R U' R' U' R U' R' U'
(1,8,3,10)(2,4,9)(5,7)  => U R U R' U' R U2 R' U' R U' R' U R U R' U R U2 R' U
(1,8,3,10)(2,4,9,7)     => U R U R2 U' R U' R' U2 R2 U R' U R U2 R' U
(1,8,10,6)(2,4,7,5)     => U R U R' U2 R U' R' U' R U' R' U R U R' U R U2 R' U
(1,8,10,6)(2,4,7,9)     => R' U' R U' R' U' U' R U' R U' R' U' R U' U' R' U' R U' R'
(1,8,10,6)(2,4,7)(5,9)  => U R U' R' U' R U2 R' U' R U' R' U R U R' U R U2 R' U
(1,8,10,6)(2,4,9,5)     => U R U R' U R U U R' U R U R' U' R' U' R U' R' U2 R U'
(1,8,10,6)(2,4,9)(5,7)  => U R U R' U R U2 R' U R U R' U R U2 R' U' R U' R' U' R U' U' R' U' R U' R'
(1,8,10,6)(2,4,9,7)     => U R U R' U R U2 R' U2 R' U2 R U R' U R U R U R'
(1,8,10,6)(2,4,5)(7,9)  => R U' R' U R U2 R' U R U R' U'
(1,8,10,6)(2,4,5,7)     => U R' U2 R U R' U R2 U' R' U2 R U' R'
(1,8,10,6)(2,4,5,9)     => U R U' R2 U' R U' R' U2 R2 U R' U R U2 R' U
(1,8,10,6)(2,4)(5,9,7)  => R' U' R U' R' U2 R U2 R U R'
(1,8,10,6)(2,4)(5,7,9)  => R' U' R U' R' U' U' R U' R U' R' U
(1,8,10,6)(2,4)         => U' R U' R' U2 R U' R'
(1,8,6,10,3)(2,9)(4,5)  => R U R' U R U U R' U R U R' U2
(1,8,6,10,3)(2,9,4,5,7) => R' U' R U' R' U2 R U2 R U' R' U'
(1,8,6,10,3)(2,9,7,4,5) => U R U R' U R U R' U' R U' R'
(1,8,6,10,3)(2,9,5,4,7) => R U R' U R U U R' U R U R2 U2 R U R' U R
(1,8,6,10,3)(2,9)(4,7)  => U R' U2 R U R' U R U2 R U' R' U' R U R'
(1,8,6,10,3)(2,9,4,7,5) => U R U R' U R U2 R' U2 R' U2 R U R' U R U R U' R' U'
(1,8,6,10,3)(2,9,7,5,4) => R U R' U R U2 R' U R U' R' U' R U' R'
(1,8,6,10,3)(2,9,4)     => R U R' U R U U R' U R U R' U R U2 R' U' R U' R' U'
(1,8,6,10,3)(2,9,5,7,4) => R U R' U R U U R' U R U R' U R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,8,6,10,3)(2,9)(5,7)  => U R U' R' U' R U R'
(1,8,6,10,3)(2,9,5)     => R' U' R U' R' U' U' R U' R U' R' U' R U2 R' U' R U R' U'
(1,8,6,10,3)(2,9,7)     => U' R U2 R' U' R U' R2 U2 R U R' U R2 U' R' U' R U' R'
(1,8,3,10)(2,9,4,5)     => R U2 U R' U R U R' U R U R' U R U2 R' U
(1,8,3,10)(2,9)(4,5,7)  => R U' R' U R U R' U' R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,8,3,10)(2,9,7)(4,5)  => R U' R' U R U R' U U R' U U R U R' U R
(1,8,3,10)(2,9,7,5)     => U2 R U' R' U2
(1,8,3,10)(2,9,5,7)     => U' R U2 R' U' R U2 R' U' R U' R' U'
(1,8,3,10)(2,9)         => R U' R' U R U R' U' R U2 R' U' R U' R' U'
(1,8,3,10)(2,9,5)(4,7)  => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U' R U' R' U' R U' R' U'
(1,8,3,10)(2,9)(4,7,5)  => R U' R' U R U R' U2 R U2 R' U' R U' R'
(1,8,3,10)(2,9,4,7)     => U R U R' U R U2 R' U R U R' U R U2 R' U R U' R' U' R U R' U'
(1,8,3,10)(2,9,5,4)     => R U' R' U R U R'
(1,8,3,10)(2,9,4)(5,7)  => R U' R' U R U R' U' R' U' R U' R' U2 R U'
(1,8,3,10)(2,9,7,4)     => U R' U2 R U R' U R U' R U' R' U2
(1,8)(2,9,4,5,7)(3,6)   => U' R U2 R' U' R U' R' U2 U' R U' R' U2 R U2 R' U'
(1,8)(2,9,7,4,5)(3,6)   => U R' U2 R U R' U R U R U' R' U2 R U' R' U' R U R'
(1,8)(2,9)(3,6)(4,5)    => U R U' R' U2 R U2 R'
(1,8)(2,9,5)(3,6)       => R U2 R' U2 R U2 R' U R U2 R' U
(1,8)(2,9)(3,6)(5,7)    => U R' U2 R U R' U R U2 R U' R' U2 R U2 R'
(1,8)(2,9,7)(3,6)       => R U' R' U2 R U' R' U' R U R'
(1,8)(2,9,7,5,4)(3,6)   => R U2 R' U2 R U R' U R U2 R' U' R U' R'
(1,8)(2,9,5,7,4)(3,6)   => R U2 R' U2 R U R' U2 R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,8)(2,9,4)(3,6)       => R U2 R' U2 R U R' U2 R U2 R' U' R U' R' U'
(1,8)(2,9,4,7,5)(3,6)   => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R2 U' R' U2 R U2 R' U'
(1,8)(2,9,5,4,7)(3,6)   => R U U R' U2 R U R' U R' U2 R U R' U R
(1,8)(2,9)(3,6)(4,7)    => U R U R' U R U2 R' U R' U' R U' R' U2 R U' R U' R' U2 R U2 R'
(1,8,10,6)(2,9,5)(4,7)  => R U R' U2 R U2 R' U' R U' R'
(1,8,10,6)(2,9,4,7)     => R U R' U2 R U2 R' U' R U' R' U R U R' U R U2 R' U
(1,8,10,6)(2,9)(4,7,5)  => R U R' U R U2 R' U' R U' R' U' R U' U' R' U' R U' R'
(1,8,10,6)(2,9,7)(4,5)  => U R' U2 R U R' U R U R U R'
(1,8,10,6)(2,9,4,5)     => R U R' U' R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,8,10,6)(2,9)(4,5,7)  => R U R' U U R' U U R U R' U R
(1,8,10,6)(2,9)         => R U R' U' R' U' R U' R' U2 R U2 R U2 R' U' R U' R' U'
(1,8,10,6)(2,9,7,5)     => R U R' U' R U2 R' U' R U' R' U'
(1,8,10,6)(2,9,5,7)     => R U R' U U R' U U R U R' U R U R U R' U R U2 R' U
(1,8,10,6)(2,9,5,4)     => R U R' U' R' U' R U' R' U2 R U'
(1,8,10,6)(2,9,4)(5,7)  => U' R U2 R' (U' R U' R' (U' R U' R' U')2
(1,8,10,6)(2,9,7,4)     => R U R'
(1,8,6,10,3)(4,5,9)     => R U R' U R U2 R' U2 R U' R' U'
(1,8,6,10,3)(4,5,7)     => U R U R' U R U2 R' U R U R' U R U R' U' R U2 R'
(1,8,6,10,3)(4,5)(7,9)  => R U' R' U2 R' U' R U' R' U2 R U2 R U2 R' U' R U' R' U'
(1,8,6,10,3)(4,7,5)     => R' U' R U' R' U2 R2 U' R' U' R U2 R'
(1,8,6,10,3)(4,7,9)     => R U' R' U R' U U R U R' U R
(1,8,6,10,3)(4,7)(5,9)  => U' R U R2 U2 R U R' U R
(1,8,6,10,3)(5,9,7)     => U' R U' R' U' R U' R' U' R U2 R' U' R U' R' U'
(1,8,6,10,3)            => R U R' U2 R U R' U U R' U2 R U R' U R
(1,8,6,10,3)(5,7,9)     => U R U' R' U' R U2 R' U' R U R' U'
(1,8,6,10,3)(4,9)(5,7)  => U' R U2 R' U' R U' R2 U2 R U R' U R U R U' R' U'
(1,8,6,10,3)(4,9,5)     => U R U R' U R U R' U U R U R' U U R' U' R U' R' U2 R U'
(1,8,6,10,3)(4,9,7)     => U R U R' U R U R' U2 R U R' U'
(1,8,3,10)(4,5)         => U' R U2 R' U' R U' R' U' R U' R' U' R U' U' R' U'
(1,8,3,10)(4,5,7,9)     => U' R U' R' U' R U R' U'
(1,8,3,10)(4,5,9,7)     => U' R U2 R' U' R U' R2 U2 R U R' U R U' R U' R' U2
(1,8,3,10)(4,7,5,9)     => U R' U2 R U R' U R2 U' R' U' R U R' U'
(1,8,3,10)(4,7)         => R U2 R' U R U R' U R' U U R U R' U R U R U R' U R U2 R' U
(1,8,3,10)(4,7,9,5)     => R U R' U R U R' U R' U' R U' R' U2 R U'
(1,8,3,10)(4,9,7,5)     => U R U R' U R U2 R' U' R U' R' U2
(1,8,3,10)(4,9)         => U R U R' U2 U R' U2 R U R' U R
(1,8,3,10)(4,9,5,7)     => R' U' R U' R' U2 R U' R U' R' U' R U' R' U'
(1,8,3,10)(5,9)         => U R U' R' U R U2 R' U R U R' U' R U2 R' U' R U' R' U'
(1,8,3,10)(5,7)         => R U2 R' U R U2 R' U R U2 R' U
(1,8,3,10)(7,9)         => R U R' U R U R' U U
(1,8)(3,6)(4,5)(7,9)    => U R U R' U R U2 R' U R U R' U R U2 R' U2 R U' R' U2 R U' R' U' R U R'
(1,8)(3,6)(4,5,7)       => R' U' R U' R' U2 R
(1,8)(3,6)(4,5,9)       => U R U' R' U R U R' U2 R U R' U'
(1,8)(3,6)(4,7,5)       => R' U2 R U R' U R
(1,8)(3,6)(4,7)(5,9)    => U R U R' U R U2 R' U R' U' R U' R' U2 R U' R U' R' U2 R U' R' U' R U R' U'
(1,8)(3,6)(4,7,9)       => U R U R' U R U2 R' U2 R' U2 R U R' U R U' R U' R' U2 R U2 R' U'
(1,8)(3,6)(4,9,5)       => U R U' R' U2 R U' R' U' R U R' U'
(1,8)(3,6)(4,9,7)       => U R U2 R' U2 R U R' U R' U' R U' R' U2 R U2 R U2 R' U' R U' R' U'
(1,8)(3,6)(4,9)(5,7)    => R' U' R U' R' U2 R R U' R' U2 R U2 R' U'
(1,8)(3,6)(5,9,7)       => R' U' R U' R' U2 R U' U' R U' R' U2 R U' R' U' R U R'
(1,8)(3,6)(5,7,9)       => R U' R' U R U R' U2 R U R' U U R' U2 R U R' U R
(1,8)(3,6)              => U R U R' U R U2 R' U R U R' U R U2 R'
(1,8,10,6)(4,7,9,5)     => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U' R U' R' U
(1,8,10,6)(4,7,5,9)     => U R U R' U R U2 R' U R U' R' U' U' R U' R' U' R U' R' U'
(1,8,10,6)(4,7)         => U R U R' U2 R U' R' U' R U' R' U' R U2 R' U' R U' R' U'
(1,8,10,6)(7,9)         => R U' R' U R U2 R' U R U2 R' U R U2 R' U
(1,8,10,6)(5,9)         => U R U' R2 U' R U' R' U2 R U2 R U2 R' U' R U' R' U'
(1,8,10,6)(5,7)         => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U' U2 R U' R' U2 R U' R'
(1,8,10,6)(4,9,5,7)     => U' R U2 R' U' R U2 R' U
(1,8,10,6)(4,9,7,5)     => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U2 R U R'
(1,8,10,6)(4,9)         => R U R' U R U' U' R' U2 R U' R' U2 R U' R' U' R U' R' U'
(1,8,10,6)(4,5,7,9)     => U' R U2 R' U' R U' R2 U2 R U R' U R U R U' R' U' U' R U' R' U' R U' R' U'
(1,8,10,6)(4,5)         => U R U R' U2 R U R' R' U2 R U R' U R
(1,8,10,6)(4,5,9,7)     => U' R U2 R' U' R U' R' U' R U R'
(1,8)(2,5,7,9,4)(3,6)   => U' R U2 R' U' R U' R2 U2 R U R' U R U' R U' R' U2 R U2 R' U'
(1,8)(2,5,4)(3,6)       => R U2 R' U' R U' R'
(1,8)(2,5,9,7,4)(3,6)   => U' R U2 R' U' R U' R2 U2 R U R' U R U R U' R' U2 R U' R' U' R U R'
(1,8)(2,5,7)(3,6)       => U R' U' R U' R' U2 R U'
(1,8)(2,5)(3,6)(7,9)    => R U R' U R U' U' R' U2 R U' R' U2 R U' R' U' R U R'
(1,8)(2,5,9)(3,6)       => U' R U2 R' U' R U2 R' U2 R U2 R'
(1,8)(2,5,7,4,9)(3,6)   => U' R U2 R' U' R U' R' U' R' U' R U' R' U2 R U' R U' R' U2 R U2 R'
(1,8)(2,5)(3,6)(4,9)    => R U R' U R U R' U2 R U2 R' U'
(1,8)(2,5,4,9,7)(3,6)   => U R U2 R' U2 R U R' U R' U' R U' R' U2 R U'
(1,8)(2,5,4,7,9)(3,6)   => R U' R' U R U R' U2 R U R' U' R' U' R U' R' U2 R U'
(1,8)(2,5,9,4,7)(3,6)   => U R U R' U R U2 R' U' R U' R' U2 R U2 R' U'
(1,8)(2,5)(3,6)(4,7)    => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R
(1,8,10,6)(2,5,7,4)     => R U R' U R U2 R' U R U' R' U2 R U' R'
(1,8,10,6)(2,5,9,4)     => U R U' R2 U' R U' R' U2 R U'
(1,8,10,6)(2,5,4)(7,9)  => R U R' U R U2 R' U2 R U R'
(1,8,10,6)(2,5,7)(4,9)  => R' U' R U' R' U2 R U' U' R U' R' U2 R U' R' U' R U' R' U'
(1,8,10,6)(2,5)(4,9,7)  => U R U R' U R U2 R' U R U R'
(1,8,10,6)(2,5,4,9)     => U R' U2 R U R' U R U2 R U' R' U' R U' U' R' U' R U' R'
(1,8,10,6)(2,5,7,9)     => U R U R' U R U2 R' U R' U' R U' R' U' U' R U' R U' R' U' R U' U' R' U' R U' R'
(1,8,10,6)(2,5)         => U R U R' U R U R' U2 R U' R'
(1,8,10,6)(2,5,9,7)     => U' R U2 R' U' R U' R2 U2 R U R' U R U R U R'
(1,8,10,6)(2,5,4,7)     => U R U R' U2 R U' R' U' R U' R'
(1,8,10,6)(2,5,9)(4,7)  => U R U' R' U' R U' U' R' U' R U' R'
(1,8,10,6)(2,5)(4,7,9)  => R U' R' U R U2 R' U R U R' U R' U2 R U R' U R U' R U2 R' U' R U' R' U'
(1,8,3,10)(2,5,4)(7,9)  => R U R' U R U R' U U2 R U R' U R U2 R' U
(1,8,3,10)(2,5,9,4)     => U R U' R' U R U2 R' U R U R'
(1,8,3,10)(2,5,7,4)     => R U R' U R U2 R' U2 R U' R' U' R U2 R' U'
(1,8,3,10)(2,5,9)(4,7)  => U R' U2 R U R' U R U2 R U' R' U2 R U' R' U' R U' R'
(1,8,3,10)(2,5,4,7)     => U' R U2 R' U' R U' R2 U2 R U R' U R U R U' R' U' R U2 R' U'
(1,8,3,10)(2,5)(4,7,9)  => U' R U2 R' U' R U' R' U' U' R U' R' U' R U R' U'
(1,8,3,10)(2,5,7)(4,9)  => U R U R' U' R U2 R' U' R U' R'
(1,8,3,10)(2,5,4,9)     => U R U R' U' R' U U R U R' U R U R U R' U R U2 R' U
(1,8,3,10)(2,5)(4,9,7)  => U R U R2 U' R U' R' U2 R U'
(1,8,3,10)(2,5,9,7)     => R' U' R U' R' U2 R2 U' R' U2
(1,8,3,10)(2,5,7,9)     => U R U' R' U' U' R U' R' U' R U' R'
(1,8,3,10)(2,5)         => U R U R' U R U2 R' U R U' R' U' R U2 R' U'
(1,8,6,10,3)(2,5,9)     => U' R U R' U R' U' R U' R' U2 R U'
(1,8,6,10,3)(2,5)(7,9)  => R U' R' U2 R' U' R U' R' U2 R U'
(1,8,6,10,3)(2,5,7)     => U R U R' U R U' U' R' U' R U' R' U' R U2 R'
(1,8,6,10,3)(2,5,7,9,4) => R U' R' U R U2 R' U' R U' R'
(1,8,6,10,3)(2,5,9,7,4) => U' R U' R' U' R U' R'
(1,8,6,10,3)(2,5,4)     => U' R U2 R' U' R U' R2 U2 R U R' U R U' R U' R' U' R U2 R'
(1,8,6,10,3)(2,5)(4,7)  => R U R' U R U R' U' R U2 R'
(1,8,6,10,3)(2,5,9,4,7) => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U' U' R U' R' U'
(1,8,6,10,3)(2,5,4,7,9) => R U' R' U R' U U R U R' U R U R U R' U R U2 R' U
(1,8,6,10,3)(2,5,7,4,9) => U R U R' U R U R' U2 R U R' U R' U2 R U R' U R
(1,8,6,10,3)(2,5,4,9,7) => U R' U2 R U R' U R2 U' R' U' R U' R'
(1,8,6,10,3)(2,5)(4,9)  => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U2 R U' R' U'
(1,3,8,6)(2,5,7,4)      => U
(1,3,8,6)(2,5,4)(7,9)   => R' U' R U' R' U2 R U' U2 R U' R' U2 R U' R' U' R U R'
(1,3,8,6)(2,5,9,4)      => R' U' R U' R' U2 R U' R U' R' U2 R U2 R' U'
(1,3,8,6)(2,5,7,9)      => U R U R' U R U2 R' U R' U' R U' R' U2 R U' U' R U' R' U2 R U' U' R'
(1,3,8,6)(2,5,9,7)      => U R U' R' U R U R' U U R U R' U R U2 R' U' R U' R' U'
(1,3,8,6)(2,5)          => U R U R' U R U2 R' U R' U' R U' R' U2 R U'
(1,3,8,6)(2,5,7)(4,9)   => U R U2 R' U2 R U R' U' R U2 R' U' R U' R' U R U R' U R U2 R' U
(1,3,8,6)(2,5)(4,9,7)   => U R U2 R' U2 R U R' U
(1,3,8,6)(2,5,4,9)      => U R' U2 R U R' U R U R U' R' U2 R U2 R'
(1,3,8,6)(2,5,4,7)      => U R' U2 R U R' U R U2
(1,3,8,6)(2,5,9)(4,7)   => R U' R' U2 R U2 R'
(1,3,8,6)(2,5)(4,7,9)   => R U' R' U R U R' U2 R U R' U'
(1,3,6,10)(2,5,9,4)     => U' R U R' U
(1,3,6,10)(2,5,4)(7,9)  => R U' R' U2
(1,3,6,10)(2,5,7,4)     => U' R U2 R' U' R U' R' U R U' R' U' R U2 R' U'
(1,3,6,10)(2,5,9,7)     => U R' U2 R U R' U R U R U' R' U2
(1,3,6,10)(2,5,7,9)     => R U' R' U R' U' R U' R' U2 R U2 R U2 R' U' R U' R' U'
(1,3,6,10)(2,5)         => U' R U2 R' U' R U' R' U' R U R' U R U R' U' R U2 R' U'
(1,3,6,10)(2,5,9)(4,7)  => R' U' R U' R' U2 R U' U2 R U' R' U2 R U' R' U' R U' R'
(1,3,6,10)(2,5)(4,7,9)  => R U R' U' R U' R' U R U R' U R U2 R' U
(1,3,6,10)(2,5,4,7)     => R U R' U2 R U R' U'
(1,3,6,10)(2,5,7)(4,9)  => U R U R' U R U2 R' U2 R U' R' U' R U R' U'
(1,3,6,10)(2,5,4,9)     => U R U R' U R U R' U U R U R' U R U2 R' U' R U' R' U'
(1,3,6,10)(2,5)(4,9,7)  => U R U R' U R U2 R' U R' U' R U' R' U2 R U2 R U' R' U2
(1,3,10,6,8)(2,5,7,9,4) => U R U R' U R U2 R' U2 R U' R' U' U' R U' R' U' R U' R' U'
(1,3,10,6,8)(2,5,4)     => R U2 R' U R U R' U R' U' R U' R' U2 R U'
(1,3,10,6,8)(2,5,9,7,4) => U R U' R' U R U2 R' U R U2 R' U R U2 R' U
(1,3,10,6,8)(2,5,9)     => U R U' R' U R U2 R' U R U R' U R' U2 R U R' U R
(1,3,10,6,8)(2,5)(7,9)  => U R' U2 R U R' U R U2 R U R'
(1,3,10,6,8)(2,5,7)     => R U' R' U2 R U' R'
(1,3,10,6,8)(2,5,7,4,9) => U R U R' U' R' U' R U' R' U2 R U2 R U2 R' U' R U' R' U'
(1,3,10,6,8)(2,5)(4,9)  => U R U R' U2 R U2 R' U' R U' R' U R U R' U R U2 R' U
(1,3,10,6,8)(2,5,4,9,7) => U R U R'
(1,3,10,6,8)(2,5,4,7,9) => R U R' U R U' R' U' R U' R' U'
(1,3,10,6,8)(2,5,9,4,7) => R U R' U R U2 R' U' R U' R' U' U' R U' R' U' R U' R' U'
(1,3,10,6,8)(2,5)(4,7)  => R U2 R' U R U' R' U' R U' R'
(1,3)(2,5,9)(8,10)      => U R U' R'
(1,3)(2,5,7)(8,10)      => U R U R' U U R U R' U
(1,3)(2,5)(7,9)(8,10)   => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R2 U' R' U' R U2 R' U' R U R'
(1,3)(2,5,7,9,4)(8,10)  => R U' R' U R U2 R' U R U R' U R' U' R U' R' U2 R U'
(1,3)(2,5,9,7,4)(8,10)  => U R U' R' U2 R U2 R' U' R U' R' U R U R' U R U2 R' U
(1,3)(2,5,4)(8,10)      => U R U R' U R U2 R' U R U R' U R U2 R' U R U' R' U2 R U' R' U'
(1,3)(2,5)(4,7)(8,10)   => U R U R' U R U2 R' U2 R' U2 R U R' U R2 U' R' U2 R U' R' U'
(1,3)(2,5,9,4,7)(8,10)  => U R U' R' U' R' U' R U' R' U2 R U2 R U2 R' U' R U' R' U'
(1,3)(2,5,4,7,9)(8,10)  => R U' R' U R U2 R' U R U2 U R' U' R U' R'
(1,3)(2,5,7,4,9)(8,10)  => U R' U2 R U R' U R U2 R U' R'
(1,3)(2,5)(4,9)(8,10)   => U' R U2 R' U' R U2 R' U' R U2 R' U' R U' R' U'
(1,3)(2,5,4,9,7)(8,10)  => U R U R' U R U U R' U R U R' U R' U U R U R' U R
(1,3,8,6)(2,7,4)(5,9)   => U' R U2 R' U' R U' R' U' R U' R' U' U' R U' R' U' R U R' U'
(1,3,8,6)(2,7,9,4)      => R U R' U R U2 R' U' R U' R' U2 R U2 R' U'
(1,3,8,6)(2,7,5,4)      => R U R' U R U2 R' U'
(1,3,8,6)(2,7)(4,5,9)   => U' R U2 R' U' R U' R2 U2 R U R' U R U2 R U' R' U2 R U2 R' U'
(1,3,8,6)(2,7,4,5)      => U R U R' U R U2 R' U2
(1,3,8,6)(2,7,9)(4,5)   => U' R U2 R' U' R U' R' U' R' U' R U' R' U2 R U' U' R U' R' U2 R U' U' R'
(1,3,8,6)(2,7,5,9)      => U' R U2 R' U' R U' R' U' R U R' U R U' U' R' U2 R U' R' U2 R U2 R'
(1,3,8,6)(2,7,9,5)      => R U' R' U R U R' U2 R U R' U R' U2 R U R' U R U' R U2 R' U' R U' R' U'
(1,3,8,6)(2,7)          => U' R U2 R' U' R U' R2 U2 R U R' U R U2
(1,3,8,6)(2,7)(4,9,5)   => U R U2 R' U2 R U R' U U2 R' U2 R U R' U R U R U R' U R U2 R' U
(1,3,8,6)(2,7,4,9)      => U' R U2 R' U' R U' R' U' R U' R' U2 R U2 R'
(1,3,8,6)(2,7,5)(4,9)   => U R U R' U R U2 R' U2 R U' R' U2 R U2 R' U'
(1,3,6,10)(2,7,5,4)     => R U R' U2 R U R' U R' U2 R U R' U R
(1,3,6,10)(2,7,9,4)     => R U' R2 U2 R U R' U R U' R U2 R' U' R U' R' U'
(1,3,6,10)(2,7,4)(5,9)  => U R U R' U R U2 R' U2 R' U2 R U R' U R R U' R' U' R U' R' U'
(1,3,6,10)(2,7,4,9)     => U R U R' U R U R' U U R U R' U R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,3,6,10)(2,7)(4,9,5)  => U R U R' U R U2 R' U R U R' U R U2 R' U R U' R' U' R U' R' U'
(1,3,6,10)(2,7,5)(4,9)  => U R U R' U R U R' U U R U R' U R' U' R U' R' U2 R U'
(1,3,6,10)(2,7)(4,5,9)  => U' R U2 R' U' R U2 R' U' R U2 U' R' U'
(1,3,6,10)(2,7,9)(4,5)  => R U' R2 U2 R U R' U R
(1,3,6,10)(2,7,4,5)     => U2 R U' R' U' R U2 R' U'
(1,3,6,10)(2,7)         => U R U R' U R U2 R' U R' U' R U' R' U2 R2 U' R' U' R U2 R' U'
(1,3,6,10)(2,7,5,9)     => U' R U2 R' U' R U' R' U' U' R U' R' U' U' R U' R' U' R U' R'
(1,3,6,10)(2,7,9,5)     => R' U' R U' R' U2 R U' U2 R U' R' U' R U' R' U'
(1,3,10,6,8)(2,7,5,9,4) => U' R U2 R' U' R U' R' U' R' U' R U' R' U2 R U' R U' R' U2 R U' R' U' R U' R' U'
(1,3,10,6,8)(2,7,9,5,4) => U' R U2 R' U' R U' R' U' R U R' U R U R' U
(1,3,10,6,8)(2,7,4)     => R U2 R' U R U R' U2
(1,3,10,6,8)(2,7)(5,9)  => U' R U2 R' U' R U' R' U2 U' R U' R' U2 U'
(1,3,10,6,8)(2,7,5)     => R U R' U R U' U' R' U2 R U' R' U2 R U' R'
(1,3,10,6,8)(2,7,9)     => R U R' U R U R2 U' R U' R' U2 R2 U R' U R U2 R' U
(1,3,10,6,8)(2,7,4,5,9) => R' U' R U' R' U2 R2 U' R' U' R U' U' R' U' R U' R'
(1,3,10,6,8)(2,7,9,4,5) => R U R' U R U R2 U' R U' R' U2 R U'
(1,3,10,6,8)(2,7)(4,5)  => U R U R' U R U2 R' U R U' R' U2 R U' R'
(1,3,10,6,8)(2,7,5,4,9) => U R U R' U U R' U U R U R' U R
(1,3,10,6,8)(2,7)(4,9)  => U R U R' U U R' U U R U R' U R U' R U2 R' U' R U' R' U'
(1,3,10,6,8)(2,7,4,9,5) => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R2 U' R' U
(1,3)(2,7)(4,5)(8,10)   => U R U R' U R U2 R' U R' U' R U' R' U2 R U' U2 R U' R' U2 R U' R' U'
(1,3)(2,7,9,4,5)(8,10)  => R' U' R U' R' U' U' R U' R U' R' U' R U' U' R' U' R U' R' U'
(1,3)(2,7,4,5,9)(8,10)  => U R U R' U R U2 R' U2 R' U2 R U R' U R U2 R U' R'
(1,3)(2,7,5,4,9)(8,10)  => U R U R' U R U2 R' U R U R' U R U2 R' U' R U' R'
(1,3)(2,7)(4,9)(8,10)   => U R U R' U R U2 R' U R U R' U R U2 R' U' R U' R' U' R U' U' R' U' R U' R' U'
(1,3)(2,7,4,9,5)(8,10)  => U R U R' U R U2 R' U2 R' U2 R U R' U R U R U R' U'
(1,3)(2,7,9,5,4)(8,10)  => R U' R' U R U2 R' U R U R' U2
(1,3)(2,7,4)(8,10)      => U R' U2 R U R' U R2 U' R' U2 R U' R' U'
(1,3)(2,7,5,9,4)(8,10)  => U R U' R' U2 R' U U R U R' U R U R U R' U R U2 R' U
(1,3)(2,7)(5,9)(8,10)   => R' U' R U' R' U2 R U2 R U R' U'
(1,3)(2,7,9)(8,10)      => R' U' R U' R' U' U' R U' R U' R'
(1,3)(2,7,5)(8,10)      => U' R U' R' U' U' R U' R' U'
(1,3,6,10)(2,9,4)(5,7)  => R U R' U R U U R' U R U R' U
(1,3,6,10)(2,9,7,4)     => R' U' R U' R' U2 R U2 R U' R' U2
(1,3,6,10)(2,9,5,4)     => U R U R' U R U R' U' R U' R' U'
(1,3,6,10)(2,9)(4,5,7)  => R U R' U R U U R' U R U R' U2 R U R' U R U2 R' U
(1,3,6,10)(2,9,4,5)     => U R' U2 R U R' U R U2 R U' R' U' R U R' U'
(1,3,6,10)(2,9,7)(4,5)  => U R U R' U R U2 R' U2 R' U2 R U R' U R U R U' R' U2
(1,3,6,10)(2,9,5,7)     => R U R' U R U2 R' U R U' R' U' R U' R' U'
(1,3,6,10)(2,9,7,5)     => U R U R' U R U2 R' U R U R' U R U2 R' U2 R U' R' U2
(1,3,6,10)(2,9)         => U R' U2 R U R' U R2 U' R' U' U' R U' R' U' R U' R'
(1,3,6,10)(2,9,4,7)     => U R U' R' U' R U R' U'
(1,3,6,10)(2,9)(4,7,5)  => U' R U' R' U' U' R U' R' U' R U' R'
(1,3,6,10)(2,9,5)(4,7)  => U' R U2 R' U' R U' R2 U2 R U R' U R R U' R' U' R U' R' U'
(1,3,10,6,8)(2,9,7,5,4) => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U' R U R'
(1,3,10,6,8)(2,9,4)     => R U' R' U R U R' U R' U U R U R' U R U R U R' U R U2 R' U
(1,3,10,6,8)(2,9,5,7,4) => R U U2 R' U R U2 R' U R U2 R' U
(1,3,10,6,8)(2,9,5,4,7) => U2 R U' R' U
(1,3,10,6,8)(2,9)(4,7)  => R U' R' U R U R' U2 R' U' R U' R' U2 R U'
(1,3,10,6,8)(2,9,4,7,5) => R' U' R U' R' U2 R U' R U' R' U2 R U' R' U' R U' R' U'
(1,3,10,6,8)(2,9)(4,5)  => U2 R U' R' U' R U' U' R' U' R U' R'
(1,3,10,6,8)(2,9,4,5,7) => R U' R' U R U R' U2 R U2 R' U' R U' R' U'
(1,3,10,6,8)(2,9,7,4,5) => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U' R U R'
(1,3,10,6,8)(2,9)(5,7)  => R U' R' U R U R' U'
(1,3,10,6,8)(2,9,7)     => U' R U2 R' U'
(1,3,10,6,8)(2,9,5)     => U R' U2 R U R' U R U' R U' R' U
(1,3,8,6)(2,9,7,4)      => R U2 R' U2 R U R' U R' U' R U' R' U2 R U'
(1,3,8,6)(2,9,5,4)      => U R' U2 R U R' U R U R U' R' U2 R U' R' U' R U R' U'
(1,3,8,6)(2,9,4)(5,7)   => U R U' R' U2 R U2 R' U'
(1,3,8,6)(2,9)(4,7,5)   => R U R' U R U' U' R' U2 R U' R' U2 R U2 R'
(1,3,8,6)(2,9,4,7)      => R U2 R' U2 R U' R' U' R U' R'
(1,3,8,6)(2,9,5)(4,7)   => R U' R' U2 R U' R' U' R U R' U'
(1,3,8,6)(2,9,5,7)      => R U2 R' U2 R U R' U R U2 R' U' R U' R' U'
(1,3,8,6)(2,9)          => U' R U2 R' U' R U' R2 U2 R U R' U R U R U' R' U2 R U2 R'
(1,3,8,6)(2,9,7,5)      => U R U R' U R U R' U2 R U' R' U' R U R'
(1,3,8,6)(2,9,7)(4,5)   => R U2 R' U2 R U R' U R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,3,8,6)(2,9)(4,5,7)   => U R U R' U R U2 R' U R U' R' U2 R U2 R'
(1,3,8,6)(2,9,4,5)      => R U2 R' U2 R U R' R' U2 R U R' U R
(1,3)(2,9)(4,5)(8,10)   => U R U R' U R U2 R' U2 R U' R'
(1,3)(2,9,7,4,5)(8,10)  => R U R' U R U' U2 R' U' R U2 R' U' R U R'
(1,3)(2,9,4,5,7)(8,10)  => R U R' U R U2 R' U' R U' R' U' R U2 R' U' R U' R' U'
(1,3)(2,9,5,7,4)(8,10)  => U R' U2 R U R' U R U R U R' U'
(1,3)(2,9,7,5,4)(8,10)  => R U R' U R' U U R U R' U R U R U R' U R U2 R' U
(1,3)(2,9,4)(8,10)      => R U2 R' U R U2 R' U
(1,3)(2,9,4,7,5)(8,10)  => R U R' U2 R' U' R U' R' U2 R U'
(1,3)(2,9,5,4,7)(8,10)  => U R U R' U R U2 R' U R' U' R U' R' U2 R U2 R U R' U'
(1,3)(2,9)(4,7)(8,10)   => U' R U2 R' U' R U' R2 U2 R U R' U R U2 R U' R'
(1,3)(2,9)(5,7)(8,10)   => R U R' U R U2 R' U' R U' R'
(1,3)(2,9,7)(8,10)      => R U R' U R' U2 R U R' U R
(1,3)(2,9,5)(8,10)      => R U R' U'
(1,3,6,10)(2,4)(5,9,7)  => R U R' U R U2 R' U2 R U' R' U2
(1,3,6,10)(2,4)         => U R U R' U R U2 R' U R U R' U R U R' U' R U2 R' U'
(1,3,6,10)(2,4)(5,7,9)  => R U' R' U R' U' R U' R' U2 R U'
(1,3,6,10)(2,4,5,7)     => R' U' R U' R' U2 R2 U' R' U' R U2 R' U'
(1,3,6,10)(2,4,5)(7,9)  => U R U R' U R U2 R' U R U' R' U2
(1,3,6,10)(2,4,5,9)     => U U2 R U R' U2 R U R' U R U2 R' U
(1,3,6,10)(2,4,7)(5,9)  => U' R U R' U' R U2 R' U' R U' R' U' R U2 R' U' R U' R' U'
(1,3,6,10)(2,4,7,5)     => R U R' U2 R U2 R' U R U2 R' U
(1,3,6,10)(2,4,7,9)     => R U R' U' R U' R' U' R U2 R' U' R U' R' U'
(1,3,6,10)(2,4,9,7)     => U R U R' U R U R' U2 R U R' R' U2 R U R' U R
(1,3,6,10)(2,4,9)(5,7)  => U R U R' U R U R' U' U' R U' R' U' R U' R'
(1,3,6,10)(2,4,9,5)     => U R U R' U R U R' U U R U R' U U
(1,3,10,6,8)(2,4)(5,7)  => R U2 R' U R U R2 U2 R U R' U R U' R U2 R' U' R U' R' U'
(1,3,10,6,8)(2,4)(7,9)  => R U R' U R U R' U U2 R' U2 R U R' U R
(1,3,10,6,8)(2,4)(5,9)  => U' R U2 R' U' R U' R2 U2 R U R' U R U' R U' R' U
(1,3,10,6,8)(2,4,5,9,7) => U R U R' U R U2 R' U2 R U R'
(1,3,10,6,8)(2,4,5)     => R U2 R' U R U R' U R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,3,10,6,8)(2,4,5,7,9) => R U R' U R U R' U' R U2 R' U' R U' R'
(1,3,10,6,8)(2,4,9,5,7) => U R U R' U' R' U' R U' R' U2 R U'
(1,3,10,6,8)(2,4,9,7,5) => R U R' U R U2 R' U' R U R'
(1,3,10,6,8)(2,4,9)     => U R U R' U R U2 R' U' R U' R' U' R U' U' R' U' R U' R'
(1,3,10,6,8)(2,4,7,5,9) => U' R U2 R' U' R U' R2 U2 R U R' U R U' R U' R' U' R U' U' R' U' R U' R'
(1,3,10,6,8)(2,4,7)     => U' R U2 R' U' R U' R' U' R U' R' U2 R U' R'
(1,3,10,6,8)(2,4,7,9,5) => R U R' U R U R' U
(1,3,8,6)(2,4)(5,7,9)   => R U' R' U R U R' U U R U R' U R U2 R' U' R U' R' U' R U2 R' U' R U' R' U'
(1,3,8,6)(2,4)          => R' U' R U' R' U2 R U'
(1,3,8,6)(2,4)(5,9,7)   => U' R U' R' U' U' R U' R' U' R U R'
(1,3,8,6)(2,4,5,7)      => U2 R U R' U R U2 R' U
(1,3,8,6)(2,4,5,9)      => U R U' R' U R U R' U2 R U R' R' U2 R U R' U R
(1,3,8,6)(2,4,5)(7,9)   => R U' R' U R U R' U U R U R' U U R' U' R U' R' U2 R U'
(1,3,8,6)(2,4,9)(5,7)   => U R U R' U R U2 R' U R U R' U R U2 R' U2 R U' R' U2 R U2 R'
(1,3,8,6)(2,4,9,5)      => U R U2 R' U2 R U R2 U' R U' R' U2 R U'
(1,3,8,6)(2,4,9,7)      => U R' U2 R U R' U R2 U' R' U2 R U' R' U' R U R'
(1,3,8,6)(2,4,7)(5,9)   => U R U' R' U R U R' U2 R U' R' U' R U' R'
(1,3,8,6)(2,4,7,9)      => R' U' R U' R' U2 R U' U' R U' R' U2 R U' U' R'
(1,3,8,6)(2,4,7,5)      => U R U R' U R U2 R' U R U R' U R U2 R' U'
(1,3)(2,4,5,7,9)(8,10)  => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U' R U' R'
(1,3)(2,4,5,9,7)(8,10)  => U2 R U' R' U' R U2 R' U' R U R'
(1,3)(2,4,5)(8,10)      => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U R U' R' U2 R U' R' U'
(1,3)(2,4,7,9,5)(8,10)  => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U2 R U R' U'
(1,3)(2,4,7,5,9)(8,10)  => U R U' R' U' R' U' R U' R' U2 R U'
(1,3)(2,4,7)(8,10)      => U R U R' U2 R U R2 U' R U' R' U2 R U'
(1,3)(2,4,9)(8,10)      => U' R U2 R' U' R U2 R'
(1,3)(2,4,9,5,7)(8,10)  => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U2 R U R' U'
(1,3)(2,4,9,7,5)(8,10)  => U R' U2 R U R' U R U' R U' R' U' R U2 R' U' R U R'
(1,3)(2,4)(7,9)(8,10)   => U R U R' U R U2 R' U R' U' R U' R' U2 R2 U' R' U' R U2 R' U' R U R'
(1,3)(2,4)(5,7)(8,10)   => U' R U2 R' U' R U' R' U' U' R U' R' U' U' R U' R' U'
(1,3)(2,4)(5,9)(8,10)   => U' R U2 R' U' R U' R' U' R U R' U'
(1,3,8,6)(7,9)          => R U' R' U R U R' U U R U R' U U R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,3,8,6)(5,7)          => R U2 R' U' R U' R' U'
(1,3,8,6)(5,9)          => U' R U2 R' U' R U' R2 U2 R U R' U R U R U' R' U2 R U' R' U' R U R' U'
(1,3,8,6)(4,7)          => U' R U2 R' U' R U' R'
(1,3,8,6)(4,7,9,5)      => R U R' U R U' U' R' U2 R U' R' U2 R U' R' U' R U R' U'
(1,3,8,6)(4,7,5,9)      => U' R U2 R' U' R U2 R' U' U' R U2 R' U'
(1,3,8,6)(4,9)          => U R U2 R' U2 R U R2 U' R U' R' U2 R2 U R' U R U2 R' U
(1,3,8,6)(4,9,7,5)      => U R U2 R' U2 R U' R' U' R U' R' U'
(1,3,8,6)(4,9,5,7)      => U R U2 R' U2 R U R' U' R U2 R' U' R U' R'
(1,3,8,6)(4,5,7,9)      => R U' R' U R U R' U U R U R' U R U2 R' U' R U' R'
(1,3,8,6)(4,5,9,7)      => U R U' R' U R U R' U2 R U R' U U2 R U R' U R U2 R' U
(1,3,8,6)(4,5)          => R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,3)(8,10)             => R U R' U R U2 R' U R U' R' U2 R U' R' U'
(1,3)(5,9,7)(8,10)      => U R U' R' U2 R U2 R' U' R U' R'
(1,3)(5,7,9)(8,10)      => R U R' U R U2 R' U2 R U R' U'
(1,3)(4,9,7)(8,10)      => U R U R' U R U2 R' U R U R' U R U' U2 R' U' R U2 R' U' R U R'
(1,3)(4,9,5)(8,10)      => U R U R' U R U2 R' U R U R' U'
(1,3)(4,9)(5,7)(8,10)   => U R' U2 R U R' U R U2 R U' R' U' R U' U' R' U' R U' R' U'
(1,3)(4,7,9)(8,10)      => R U' R' U R U2 R' U R U2 U R' U' R U' R' U' R U2 R' U' R U' R' U'
(1,3)(4,7,5)(8,10)      => U R U R' U R U R' U2 R U' R' U'
(1,3)(4,7)(5,9)(8,10)   => U' R U2 R' U' R U' R2 U2 R U R' U R U R U R' U'
(1,3)(4,5,7)(8,10)      => U R U R' U2 R U' R' U' R U' R' U'
(1,3)(4,5,9)(8,10)      => U R U' R' U' R U' U' R' U' R U' R' U'
(1,3)(4,5)(7,9)(8,10)   => R' U' R U' R' U2 R2 U' R' U' R U2 R' U' R U R'
(1,3,10,6,8)(5,7,9)     => U R U R' U R U2 R' U R U R' U R U R' U
(1,3,10,6,8)(5,9,7)     => U R U' R' U R U2 R' U R U R' U'
(1,3,10,6,8)            => R' U' R U' R' U2 R U' U' R U' R' U2 R U' R'
(1,3,10,6,8)(4,5,9)     => U R' U2 R U R' U R U2 R U' R' U2 R U' R' U' R U' R' U'
(1,3,10,6,8)(4,5,7)     => R U2 R' U R U R2 U2 R U R' U R
(1,3,10,6,8)(4,5)(7,9)  => U R U R' U R U2 R' U2 R' U2 R U R' U R U2 R U R'
(1,3,10,6,8)(4,9,7)     => R' U' R U' R' U' U' R U' R U R'
(1,3,10,6,8)(4,9)(5,7)  => U R U R' U' R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,3,10,6,8)(4,9,5)     => U R U R' U2 R U2 R' U' R U' R'
(1,3,10,6,8)(4,7)(5,9)  => R' U' R U' R' U2 R2 U' R' U
(1,3,10,6,8)(4,7,9)     => U R U' R' U' U' R U' R' U' R U' R' U'
(1,3,10,6,8)(4,7,5)     => R U2 R' U R U' R' U' R U' R' U' R U2 R' U' R U' R' U'
(1,3,6,10)(4,7,5,9)     => U' R U R' U' R U2 R' U' R U' R'
(1,3,6,10)(4,7,9,5)     => R U R' U' R U' R'
(1,3,6,10)(4,7)         => U R U R' U R U' U' R' U' R U' R' U' R U2 R' U'
(1,3,6,10)(7,9)         => R U' R' U R U2 R' U' R U' R' U'
(1,3,6,10)(5,9)         => U' R U' R' U' R U' R' U'
(1,3,6,10)(5,7)         => U' R U2 R' U' R U' R2 U2 R U R' U R U' R U' R' U' R U2 R' U'
(1,3,6,10)(4,5)         => R U R' U R U R' U' R U2 R' U'
(1,3,6,10)(4,5,9,7)     => U' R U R2 U' R U' R' U2 R2 U R' U R U2 R' U
(1,3,6,10)(4,5,7,9)     => R U' R' U R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,3,6,10)(4,9)         => U R U R' U R U R' U2 R U R' U U2 R U R' U R U2 R' U
(1,3,6,10)(4,9,5,7)     => U R' U2 R U R' U R R U' R' U' R U' R' U'
(1,3,6,10)(4,9,7,5)     => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U2 R U' R' U2
(1,10,8,3,6)(2,7,5,4,9) => U' R U' R'
(1,10,8,3,6)(2,7,4,9,5) => U R U R' U R U2 R' U R' U' R U' R' U2 R2 U R' U'
(1,10,8,3,6)(2,7)(4,9)  => U' R U' R' U' R U' U' R' U' R U' R' U'
(1,10,8,3,6)(2,7,9,5,4) => U2 R U R' U'
(1,10,8,3,6)(2,7,4)     => R' U' R U' R' U2 R U' R U' R' U2 R U' R' U'
(1,10,8,3,6)(2,7,5,9,4) => U R U R' U R U R' U' R' U' R U' R' U2 R U2 R U2 R' U' R U' R' U'
(1,10,8,3,6)(2,7)(4,5)  => U R U2 R' U R U R' U' R U2 R' U' R U' R' U R U R' U R U2 R' U
(1,10,8,3,6)(2,7,4,5,9) => U R U R' U R U R' U' R' U' R U' R' U2 R U'
(1,10,8,3,6)(2,7,9,4,5) => U2 R U2 R' U R U2 R' U
(1,10,8,3,6)(2,7,9)     => U R' U2 R U R' U R2 U' R'
(1,10,8,3,6)(2,7,5)     => U R U R' U R U2 R' U R U R' U R U2 R' U' R U' R' U2 R U' R' U'
(1,10,8,3,6)(2,7)(5,9)  => U R' U2 R U R' U R U' R U R' U'
(1,10,6,3)(2,7,4,9)     => U R U' R' U R U R' U'
(1,10,6,3)(2,7,5)(4,9)  => U R U' R' U R U R' U2 R U2 R' U' R U' R' U'
(1,10,6,3)(2,7)(4,9,5)  => R' U' R U' R' U2 R U' U2 R U' R' U
(1,10,6,3)(2,7,5,4)     => U R U2 R' U R U R2 U2 R U R' U R
(1,10,6,3)(2,7,4)(5,9)  => U R U R' U R U2 R' U R U R' U R U2 R' U R U' R' U
(1,10,6,3)(2,7,9,4)     => R' U' R U' R' U2 R R U' R' U2 R U' R' U' R U' R' U'
(1,10,6,3)(2,7)         => U R U R' U R U2 R' U R' U' R U' R' U2 R U' R U' R' U2 R U' R'
(1,10,6,3)(2,7,5,9)     => U R U R' U R U R' U' R U2 R' U' R U' R'
(1,10,6,3)(2,7,9,5)     => U2 R U R' U' R' U' R U' R' U2 R U'
(1,10,6,3)(2,7,4,5)     => U R U' R' U2 R U' R'
(1,10,6,3)(2,7,9)(4,5)  => U2 R U R' U' R' U' R U' R' U2 R U2 R U2 R' U' R U' R' U'
(1,10,6,3)(2,7)(4,5,9)  => U R U R' U R U R' U' R U2 R' U' R U' R' U' R U2 R' U' R U' R' U'
(1,10)(2,7)(4,9)(6,8)   => U R' U2 R U R' U R U R U' R' U' R U R' U'
(1,10)(2,7,4,9,5)(6,8)  => U' R U2 R' U' R U' R' U' R U R' U R U R' U' R U' R' U'
(1,10)(2,7,5,4,9)(6,8)  => U R' U2 R U R' U R U' R U' R' U' U' R U' R' U' R U' R'
(1,10)(2,7,4)(6,8)      => U R U2 R' U R U2 R' U R U2 R' U
(1,10)(2,7,9,5,4)(6,8)  => U' R U2 R' U' R U' R' U2 U' R U' R' U' R U' R' U'
(1,10)(2,7,5,9,4)(6,8)  => R U' R' U' R U R' U'
(1,10)(2,7,9)(6,8)      => U2 R U R' U' R U2 R' U' R U' R' U R U R' U R U2 R' U
(1,10)(2,7)(5,9)(6,8)   => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R R U' R' U' R U' R' U'
(1,10)(2,7,5)(6,8)      => U R U2 R' U R U R' U'
(1,10)(2,7,9,4,5)(6,8)  => U2 R U R' U' R U2 R' U' R U' R'
(1,10)(2,7)(4,5)(6,8)   => U R U R' U R U2 R' U2 R U' R' U' R U2 R' U'
(1,10)(2,7,4,5,9)(6,8)  => U2 R U' R' U2 R U' R' U' R U' R'
(1,10,3,8)(2,7,5,4)     => U R U' R' U' R U2 R'
(1,10,3,8)(2,7,9,4)     => U' R U2 R' U' R U' R2 U2 R U R' U R2 U' R' U'
(1,10,3,8)(2,7,4)(5,9)  => U R U R' U R U R' U2 R U2 R' U' R U' R' U'
(1,10,3,8)(2,7)(4,5,9)  => U R U R' U R U R' U'
(1,10,3,8)(2,7,4,5)     => U R U R' U R U2 R' U R' U' R U' R' U' U' R U' R U' R' U' R U2 R'
(1,10,3,8)(2,7,9)(4,5)  => R' U' R U' R' U2 R U2 R U' R' U' R U R'
(1,10,3,8)(2,7)(4,9,5)  => U R U' R' U R U R' U' R U2 R' U' R U' R'
(1,10,3,8)(2,7,5)(4,9)  => R U R' U R U2 R' U R U' R' U'
(1,10,3,8)(2,7,4,9)     => U R U R' U R U2 R' U R U R' U R U2 R' U2 R U' R' U' R U R'
(1,10,3,8)(2,7,5,9)     => U R U R' U R U2 R' U R U2 R' U
(1,10,3,8)(2,7)         => U R' U2 R U R' U R U2 R U' R' U' R U2 R'
(1,10,3,8)(2,7,9,5)     => U2 R U R2 U2 R U R' U R
(1,10,8,3,6)(2,4,9)     => R U R' U R U2 R' U R U' R'
(1,10,8,3,6)(2,4,9,5,7) => U' R U2 R' U' R U' R2 U2 R U R' U R U' R U R' U'
(1,10,8,3,6)(2,4,9,7,5) => U R U' R' U R U R' U R' U' R U' R' U2 R U'
(1,10,8,3,6)(2,4,7)     => U' R U2 R' U' R U' R2 U2 R U R' U R U2 R U' R' U2 R U' R' U'
(1,10,8,3,6)(2,4,7,5,9) => U R U R' U R U R'
(1,10,8,3,6)(2,4,7,9,5) => U R U R' U R U2 R' U' R U R' U'
(1,10,8,3,6)(2,4)(7,9)  => U2 R U R' U R' U2 R U R' U R U' R U2 R' U' R U' R' U'
(1,10,8,3,6)(2,4)(5,9)  => R U R' U R U' R' U'
(1,10,8,3,6)(2,4)(5,7)  => U R U2 R' U R U' R' U' R U' R' U'
(1,10,8,3,6)(2,4,5,7,9) => U' R U2 R' U' R U' R2 U2 R U R' U R2 U' R'
(1,10,8,3,6)(2,4,5)     => U R U R' U R U2 R' U2 R U' R' U2 R U' R' U'
(1,10,8,3,6)(2,4,5,9,7) => U R U R' U R U R' U2 R U2 R' U' R U' R'
(1,10,6,3)(2,4,9,5)     => U' R U' R' U
(1,10,6,3)(2,4,9)(5,7)  => U' R U' R' U' R U' U' R' U' R U' R'
(1,10,6,3)(2,4,9,7)     => U R U R' U R U2 R' U R' U' R U' R' U2 R2 U R'
(1,10,6,3)(2,4,5)(7,9)  => U2 R U R'
(1,10,6,3)(2,4,5,7)     => R' U' R U' R' U2 R U' R U' R' U2 R U' R'
(1,10,6,3)(2,4,5,9)     => U R U R' U R U' R' U' R U' R' U'
(1,10,6,3)(2,4,7,5)     => U R U2 R' U R U R' U' R U R' U R U2 R' U
(1,10,6,3)(2,4,7,9)     => U2 R U R' U U R' U U R U R' U R
(1,10,6,3)(2,4,7)(5,9)  => U R U R' U R U2 R' U R' U' R U' R' U2 R U' U2 R U' R' U
(1,10,6,3)(2,4)         => U R U2 R' U R U' R' U' R U' R' U' R U2 R' U' R U' R' U'
(1,10,6,3)(2,4)(5,7,9)  => U R' U2 R U R' U R2 U' R' U
(1,10,6,3)(2,4)(5,9,7)  => U R' U2 R U R' U R U' R U R'
(1,10)(2,4,9,5,7)(6,8)  => U R U' R' U R U R'
(1,10)(2,4,9,7,5)(6,8)  => R' U' R U' R' U2 R U' U2 R U' R' U2
(1,10)(2,4,9)(6,8)      => U R U' R' U R U R' U2 R U2 R' U' R U' R'
(1,10)(2,4,5)(6,8)      => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U' R U' R' U' R U2 R' U'
(1,10)(2,4,5,7,9)(6,8)  => R' U' R U' R' U2 R R U' R' U2 R U' R' U' R U' R'
(1,10)(2,4,5,9,7)(6,8)  => U R U R' U R U R' U' R U R' U R U2 R' U
(1,10)(2,4)(6,8)(7,9)   => U R U R' U R U2 R' U2 R' U2 R U R' U R2 U' R' U2
(1,10)(2,4)(5,7)(6,8)   => U' R U2 R' U' R U' R' U' R U R' U R U' U' R' U' R U' R' U' R U2 R' U'
(1,10)(2,4)(5,9)(6,8)   => U R' U2 R U R' U R U' R U' R' U' R U' R' U'
(1,10)(2,4,7,9,5)(6,8)  => U' U' R U' R' U' R U' R' U'
(1,10)(2,4,7)(6,8)      => U' R U2 R' U' R U2 R' U' R U2 R' U'
(1,10)(2,4,7,5,9)(6,8)  => U R U R' U R U' R' U' R U' R' U' R U2 R' U' R U' R' U'
(1,10,3,8)(2,4,7,5)     => U R U R' U R U2 R' U2 R U' R' U' R U2 R'
(1,10,3,8)(2,4,7)(5,9)  => U R U R' U R U R' U R' U2 R U R' U R U' R U2 R' U' R U' R' U'
(1,10,3,8)(2,4,7,9)     => U2 R U R' U R' U' R U' R' U2 R U'
(1,10,3,8)(2,4,9,7)     => U R U' R' U R U' R' U' R U' R' U'
(1,10,3,8)(2,4,9,5)     => R U' R' U' R U2 R' U' R U R' U'
(1,10,3,8)(2,4,9)(5,7)  => U R' U2 R U R' U R U R U' R' U' R U R'
(1,10,3,8)(2,4,5,9)     => R U' R' U' R U R'
(1,10,3,8)(2,4,5)(7,9)  => U' R U2 R' U' R U' R' U2 U' R U' R' U' R U' R'
(1,10,3,8)(2,4,5,7)     => U R U2 R' U R U R' U U R' U U R U R' U R
(1,10,3,8)(2,4)         => U R U2 R' U R U R'
(1,10,3,8)(2,4)(5,7,9)  => U2 R U R' U U2 R U R' U R U2 R' U
(1,10,3,8)(2,4)(5,9,7)  => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R2 U' R' U' R U' R'
(1,10,8,3,6)(2,5,7,4,9) => R' U' R U' R' U2 R U' U2 R U' R'
(1,10,8,3,6)(2,5)(4,9)  => U R U' R' U R U R' U2
(1,10,8,3,6)(2,5,4,9,7) => R U R' U R U2 R' U2 R U' R' U' R U2 R' U' R U R'
(1,10,8,3,6)(2,5,7)     => U R' U2 R U R' U R U2 R U' R' U2 R U' R' U'
(1,10,8,3,6)(2,5)(7,9)  => U2 R U R' U R' U U R U R' U R U R U R' U R U2 R' U
(1,10,8,3,6)(2,5,9)     => U R U R' U R U2 R' U R U R' U R U2 R' U R U' R'
(1,10,8,3,6)(2,5,7,9,4) => U2 R U R' U2 R' U' R U' R' U2 R U'
(1,10,8,3,6)(2,5,4)     => U R U' R' U2 R U' R' U'
(1,10,8,3,6)(2,5,9,7,4) => U R U R' U R U2 R' U R U' R' U' R U2 R' U' R U R'
(1,10,8,3,6)(2,5,4,7,9) => U2 R U R' U R U2 R' U' R U' R'
(1,10,8,3,6)(2,5)(4,7)  => U R U2 R' U R U R' U2 U R' U2 R U R' U R
(1,10,8,3,6)(2,5,9,4,7) => U R U R' U R U R' U' R U2 R' U' R U' R' U'
(1,10,6,3)(2,5,4,9)     => U R U' R' U R U R' U2 R' U' R U' R' U2 R U'
(1,10,6,3)(2,5,7)(4,9)  => U R' U2 R U R' U R U' R U' R' U' U' R U' R' U' R U' R' U'
(1,10,6,3)(2,5)(4,9,7)  => U' R U2 R' U' R U' R' U' R U R' U R U' R'
(1,10,6,3)(2,5,4,7)     => U R U2 R' U R U R' U2
(1,10,6,3)(2,5,9)(4,7)  => U R U R' U R U R' R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,10,6,3)(2,5)(4,7,9)  => U2 R U R' U U R' U U R U R' U R U' R U2 R' U' R U' R' U'
(1,10,6,3)(2,5,4)(7,9)  => U' R U2 R' U' R U' R' U R U R'
(1,10,6,3)(2,5,9,4)     => U2 R U' R' U2 R U' R' U' R U' R' U'
(1,10,6,3)(2,5,7,4)     => U' R U2 R' U' R U2 R' U2 R U' R'
(1,10,6,3)(2,5)         => U R U2 R' U R U' R' U' R U' R' U R U R' U R U2 R' U
(1,10,6,3)(2,5,7,9)     => U2 R U R' U2 R U2 R' U' R U' R' U' R U2 R' U' R U' R' U'
(1,10,6,3)(2,5,9,7)     => U R U R' U R U R' U' R' U2 R U R' U R
(1,10)(2,5,4,9,7)(6,8)  => R U R' U R U2 R' U R U' R' U2
(1,10)(2,5)(4,9)(6,8)   => U R U R' U R U2 R' U R U R' U R U2 R' U2 R U' R' U' R U R' U'
(1,10)(2,5,7,4,9)(6,8)  => U R U' R' U R U R' U' R U2 R' U' R U' R' U'
(1,10)(2,5,4)(6,8)      => U R U R' U R U2 R' U R' U' R U' R' U' U' R U' R U' R' U' R U2 R' U'
(1,10)(2,5,9,7,4)(6,8)  => U R U R' U R U R' U2
(1,10)(2,5,7,9,4)(6,8)  => U2 R U R' U2 U R' U2 R U R' U R
(1,10)(2,5,4,7,9)(6,8)  => U2 R U R' U2 R U R' U R U2 R' U
(1,10)(2,5,9,4,7)(6,8)  => U R U R' U R U' R' U' R U' R' U R U R' U R U2 R' U
(1,10)(2,5)(4,7)(6,8)   => U R' U2 R U R' U R U2 R U' R' U' R U2 R' U'
(1,10)(2,5)(6,8)(7,9)   => U' R U2 R' U' R U' R2 U2 R U R' U R2 U' R' U2
(1,10)(2,5,7)(6,8)      => U R U' R' U' R U2 R' U'
(1,10)(2,5,9)(6,8)      => U' R U2 R' U' R U' R' U' R U R' U R U R' U' U' R U' R' U' R U' R'
(1,10,3,8)(2,5,9,7)     => R U R' U R U R' U' R U' R'
(1,10,3,8)(2,5)         => U R U2 R' U R U R' U' R U2 R' U' R U' R' U'
(1,10,3,8)(2,5,7,9)     => U2 R U R' U2
(1,10,3,8)(2,5,7,4)     => R' U' R U' R' U' U' R U' R U' R' U' R U2 R'
(1,10,3,8)(2,5,4)(7,9)  => U R U R' U R U' U' R' U' R U' R' U' R U' R'
(1,10,3,8)(2,5,9,4)     => U R U R' U R U R' U R U2 R' U' R U' R'
(1,10,3,8)(2,5,7)(4,9)  => U' R U' R' U'
(1,10,3,8)(2,5,4,9)     => U' R U2 R' U' R U' R' U' R U' R' U' R U' U2 R'
(1,10,3,8)(2,5)(4,9,7)  => U R U' R' U R U R' U U R U R' U R U2 R' U
(1,10,3,8)(2,5,9)(4,7)  => U R U R' U R U R' U R' U U R U R' U R U R U R' U R U2 R' U
(1,10,3,8)(2,5,4,7)     => U R U R' U R U2 R' U2 R' U2 R U R' U R U2 R U' R' U' R U2 R'
(1,10,3,8)(2,5)(4,7,9)  => U R' U2 R U R' U R2 U' R' U'
(1,10,6,3)(4,9)         => U' R U2 R' U' R U' R' U2 U' R U' R' U2 R U' R' U' R U' R' U'
(1,10,6,3)(4,9,5,7)     => R U R' U R U2 R' U R U' R' U
(1,10,6,3)(4,9,7,5)     => U' R U2 R' U' R U' R2 U2 R U R' U R U' R U R'
(1,10,6,3)(4,7)         => U R U R' U R U2 R' U2 R U' R' U2 R U' R'
(1,10,6,3)(4,7,9,5)     => U' R U2 R' U' R U' R2 U2 R U R' U R2 U' R' U
(1,10,6,3)(4,7,5,9)     => U R U R' U R U R' R' U' R U' R' U2 R U'
(1,10,6,3)(7,9)         => U R U R' U R U2 R' U' R U R'
(1,10,6,3)(5,9)         => U R U R' U R U R' U
(1,10,6,3)(5,7)         => U' R U2 R' U' R U' R2 U2 R U R' U R U2 R U' R' U2 R U' R'
(1,10,6,3)(4,5)         => U R U2 R' U R U' R' U' R U' R'
(1,10,6,3)(4,5,7,9)     => U2 R U R' U2 R U2 R' U' R U' R' U R U R' U R U2 R' U
(1,10,6,3)(4,5,9,7)     => R U R' U R U' R'
(1,10)(4,9,7)(6,8)      => U' R U' R' U2
(1,10)(4,9)(5,7)(6,8)   => U' R U2 R' U' R U' R' U' R U' R' U' R U' U2 R' U'
(1,10)(4,9,5)(6,8)      => U' R U2 R' U' R U' R2 U2 R U R' U R U' R U' R' U' R U' R' U'
(1,10)(4,7,5)(6,8)      => U R U R' U R U2 R' U R U R' U R U2 R' U' R U' R' U' R U2 R' U'
(1,10)(4,7)(5,9)(6,8)   => R U R' U R U R' U' R U' R' U'
(1,10)(4,7,9)(6,8)      => U2 R U R' U
(1,10)(6,8)             => R' U' R U' R' U' U' R U' R U' R' U' R U2 R' U'
(1,10)(5,9,7)(6,8)      => U R U R' U R U R' U R U2 R' U' R U' R' U'
(1,10)(5,7,9)(6,8)      => U R U R' U R U' U' R' U' R U' R' U' R U' R' U'
(1,10)(4,5)(6,8)(7,9)   => U R' U2 R U R' U R2 U' R' U2
(1,10)(4,5,7)(6,8)      => U R U2 R' U R U R' U R U2 R' U' R U' R' U' R U2 R' U' R U' R' U'
(1,10)(4,5,9)(6,8)      => U R U R' U R U R' U R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,10,8,3,6)(4,9,5)     => U' R U2 R' U' R U' R' U' R U R' U R U' R' U'
(1,10,8,3,6)(4,9)(5,7)  => U R U' R' U R U' R' U' R U' R'
(1,10,8,3,6)(4,9,7)     => R U' R' U' R U2 R' U' R U R'
(1,10,8,3,6)(4,7,5)     => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U' R U' R' U' U' R U' R' U'
(1,10,8,3,6)(4,7,9)     => U2 R U R' U R U2 R' U' R U' R' U' R U2 R' U' R U' R' U'
(1,10,8,3,6)(4,7)(5,9)  => U R U R' U R U R' U R U R' U R U2 R' U
(1,10,8,3,6)(4,5)(7,9)  => U2 R U R' U R' U2 R U R' U R
(1,10,8,3,6)(4,5,9)     => U R U R' U R U R' U2 R' U U R U R' U R U R U R' U R U2 R' U
(1,10,8,3,6)(4,5,7)     => U R U2 R' U R U R' U
(1,10,8,3,6)(5,7,9)     => U' R U2 R' U' R U' R' U R U R' U'
(1,10,8,3,6)            => U' R U2 R' U' R U2 R' U2 R U' R' U'
(1,10,8,3,6)(5,9,7)     => U R U R' U R U R' U2 R U2 R' U' R U' R' U R U R' U R U2 R' U
(1,10,3,8)(4,7)         => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U' R U' R' U' R U2 R'
(1,10,3,8)(4,7,9,5)     => U2 R U R' U R' U' R U' R' U2 R2 U R' U R U2 R' U
(1,10,3,8)(4,7,5,9)     => U R U R' U R U R' U R' U2 R U R' U R
(1,10,3,8)(5,9)         => U R U R' U R U2 R' U R U' R' U' R U2 R' U' R U R' U'
(1,10,3,8)(5,7)         => U' R U2 R' U' R U2 R' U' R U2 R'
(1,10,3,8)(7,9)         => U' U' R U' R' U' R U' R'
(1,10,3,8)(4,9)         => R' U' R U' R' U2 R U' U2 R U' R' U'
(1,10,3,8)(4,9,5,7)     => U R U' R' U R U R2 U' R U' R' U2 R U'
(1,10,3,8)(4,9,7,5)     => U R U' R' U R U R' U
(1,10,3,8)(4,5,9,7)     => U R' U2 R U R' U R U' R U' R' U' R U' R'
(1,10,3,8)(4,5)         => U R U U R' U R U R' U R U R' U R U2 R' U
(1,10,3,8)(4,5,7,9)     => U2 R U R' U R U2 R' U' R U' R' U'
(1,10,8,3,6)(2,9,5,7,4) => R' U' R U' R' U2 R2 U R' U'
(1,10,8,3,6)(2,9,4)     => R U R' U R U R' U U R U R'
(1,10,8,3,6)(2,9,7,5,4) => R U R' U R U R' U U R U R' U' R' U' R U' R' U2 R U'
(1,10,8,3,6)(2,9)(5,7)  => U' R U2 R' U' R U' R' U2 R U' R'
(1,10,8,3,6)(2,9,7)     => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U2 R U' R' U' R U2 R' U' R U R'
(1,10,8,3,6)(2,9,5)     => U R U R' U R U2 R' U R U R' U R U' R' U'
(1,10,8,3,6)(2,9,4,5,7) => R U R' U R U R' U2 R U R' U U R' U2 R U R' U R
(1,10,8,3,6)(2,9)(4,5)  => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U R U' R'
(1,10,8,3,6)(2,9,7,4,5) => U' R U2 R' U' R U' R' U' R U' R' U' R U' U' R' U' R U R'
(1,10,8,3,6)(2,9,5,4,7) => U R U R' U R U2 R' U2 R' U2 R U R' U R U' R U R' U'
(1,10,8,3,6)(2,9)(4,7)  => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U R U' R'
(1,10,8,3,6)(2,9,4,7,5) => R U R' U R U R' U U R U R' U U R U2 R' U' R U' R'
(1,10)(2,9,7,5,4)(6,8)  => R U R' U R U R' U2 R U R' R' U2 R U R' U R
(1,10)(2,9,5,7,4)(6,8)  => U R U R' U R U2 R' U R U R' U R U R' U' R U' R' U'
(1,10)(2,9,4)(6,8)      => R U R' U R U2 R' U2 R U' R' U' R U R' U'
(1,10)(2,9,5,4,7)(6,8)  => R U R' U R U R' U U R U R' U U
(1,10)(2,9,4,7,5)(6,8)  => U R U R' U R U2 R' U R U' R' U' R U R' U'
(1,10)(2,9)(4,7)(6,8)   => U R U R' U R U2 R' U' R U' R' U' U' R U' R' U' R U' R'
(1,10)(2,9)(4,5)(6,8)   => R U R' U R U R' U' U' R U' R' U' R U' R'
(1,10)(2,9,7,4,5)(6,8)  => U' R U2 R' U' R U' R' U' U' R U' R' U' U'
(1,10)(2,9,4,5,7)(6,8)  => R U R' U R U R' U U R U R' U R' U' R U' R' U2 R U'
(1,10)(2,9,7)(6,8)      => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U R U' R' U2
(1,10)(2,9)(5,7)(6,8)   => U' R U2 R' U' R U' R2 U2 R U R' U R U' R U' R' U' U' R U' R' U' R U' R'
(1,10)(2,9,5)(6,8)      => U R U R' U R U2 R' U2 R' U2 R U R' U R U' R U' R' U' R U' R' U'
(1,10,3,8)(2,9,7,4)     => R U R' U R U R' U U R U2 R' U R U2 R' U
(1,10,3,8)(2,9,4)(5,7)  => U' R U2 R' U' R U' R' U' R U R' U R U2 R' U R U' R' U'
(1,10,3,8)(2,9,5,4)     => U' R U2 R' U' R U' R' U' R U' R' U' R U' U' R' U' R U R' U'
(1,10,3,8)(2,9,5,7)     => R U R' U R U R' U U R U R' U R U2 R' U' R U' R'
(1,10,3,8)(2,9)         => U R U R' U R U2 R' U R U' R' U' R U R'
(1,10,3,8)(2,9,7,5)     => R U R' U R U R' U U R U R' U'
(1,10,3,8)(2,9)(4,7,5)  => U' R U2 R' U' R U' R2 U2 R U R' U R U R U' R' U' R U R'
(1,10,3,8)(2,9,4,7)     => U' R U2 R' U' R U' R' U' U' R U' R' U'
(1,10,3,8)(2,9,5)(4,7)  => R U R' U R U R' U U R U R' U U R' U' R U' R' U2 R U'
(1,10,3,8)(2,9)(4,5,7)  => R U R' U R U2 R' U2 R U' R' U' R U R'
(1,10,3,8)(2,9,7)(4,5)  => U R U R' U R U2 R' U R U R' U R U R' U' R U' R'
(1,10,3,8)(2,9,4,5)     => U' R U2 R' U' R U' R' U' R' U' R U' R' U' U' R U R U' R' U'
(1,10,6,3)(2,9,7,5)     => U R U R' U R U2 R' U2 R' U2 R U R' U R U' R U R'
(1,10,6,3)(2,9)         => R U R' U R U R' U U R U R2 U' R U' R' U2 R U'
(1,10,6,3)(2,9,5,7)     => R U R' U R U R' U U R U R' U U R U R' U R U2 R' U
(1,10,6,3)(2,9)(4,5,7)  => R U R' U R U R' U U R U R' U
(1,10,6,3)(2,9,7)(4,5)  => R' U' R U' R' U2 R2 U R'
(1,10,6,3)(2,9,4,5)     => U R U R' U R U2 R' U' R U' R' U' U' R U' R' U' R U' R' U'
(1,10,6,3)(2,9,4)(5,7)  => R U R' U R U R' U' U' R U' R' U' R U' R' U'
(1,10,6,3)(2,9,5,4)     => U' R U2 R' U' R U' R' U' U' R U' R' U' U2
(1,10,6,3)(2,9,7,4)     => U R U R' U R U2 R' U R U R' U R U' R'
(1,10,6,3)(2,9,5)(4,7)  => R U R' U R U R' U U R U R' U U2 R' U2 R U R' U R
(1,10,6,3)(2,9)(4,7,5)  => U' R U2 R' U' R U' R' U' U' R U' R' U' R U2 R' U' R U' R'
(1,10,6,3)(2,9,4,7)     => U' R U2 R' U' R U' R2 U2 R U R' U R U' R U' R' U' U' R U' R' U' R U' R' U'

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