山折り谷折り〜横へな 2014.2.1 参考問題

問題

紙を何度か折ってから広げると、山折りと谷折の跡がつく。
山折りと谷折りがどんな順序でできるのかを計算せよ。

紙の折り方は、以下の5種類。

記号	折り方	図
L	縦に二つ折り。右側を固定。中央を谷折り。
J	縦に二つ折り。左側を固定。中央を谷折り。
Z	縦に三つ折り。右側を固定。右側は谷折り、左側は山折り。
U	縦に三つ折り。中央を固定。右も左も谷折り。
S	縦に三つ折り。左側を固定。右側は山折り、左側は谷折り。

例えば。
JZ と折ると、

という具合になる。これを開くと

こんな具合になるので、折り目は左から順に
山, 谷, 谷, 山, 谷
となる。

入力と出力

入力は JZ こんな感じ。折り方の記号を、折る順序のとおりに区切り文字なしで並べたもの。
J L Z U S のいずれかの文字のみで構成される。

出力は mVVmV こんな感じ。
山折りを m , 谷折りを V で表現し、折り目の向きを左から順に記載する。
こちらも区切り文字はない。

補足

折り目がない場合の処理は考えなくて良い。つまり、入力文字列は空文字ではない。
折り目の数が 120 個ぐらいまで対応できれば良い。
不正な入力に対処する必要はない。
ちなみに、m は「山折り」の英語「mountain fold」のm。V は谷折りの英語「valley fold」の V。谷折りだけ大文字なのは、ぱっと見区別がしやすいように。
実装ができた方は Qiitaの記事のコメント欄からリンクを張っていただくと見つけやすくて助かります。
この問題は2014年2月1日に開催される第18回オフラインリアルタイムどう書くの参考問題です。イベントについては ATND の募集ページの方を御覧下さい。
参考問題ではありますが、似たような問題が出ることはあまりありません。

サンプルデータ

#	入力	期待
0	`JZ`	`mVVmV`
1	`J`	`V`
2	`L`	`V`
3	`Z`	`mV`
4	`U`	`VV`
5	`S`	`Vm`
6	`JL`	`VVm`
7	`JS`	`VmVVm`
8	`JU`	`VVVmm`
9	`LU`	`mmVVV`
10	`SL`	`VVmmV`
11	`SS`	`VmVVmmVm`
12	`SU`	`VVVmmmVV`
13	`SZ`	`mVVmVmmV`
14	`UL`	`mVVVm`
15	`UU`	`mmVVVVmm`
16	`UZ`	`mVVmVVmV`
17	`ZJ`	`VmmVV`
18	`ZS`	`VmmVmVVm`
19	`ZZ`	`mVmmVVmV`
20	`JJJ`	`VVmVVmm`
21	`JJZ`	`mVVmVVmVmmV`
22	`JSJ`	`VVmmVVmVVmm`
23	`JSS`	`VmVVmmVmVVmVVmmVm`
24	`JUS`	`VmVVmVVmVVmmVmmVm`
25	`JUU`	`mmVVVVmmVVVmmmmVV`
26	`JUZ`	`mVVmVVmVVmVmmVmmV`
27	`LJJ`	`VmmVVVm`
28	`LLS`	`VmmVmVVmVVm`
29	`LLU`	`mmmVVVmmVVV`
30	`LLZ`	`mVmmVVmVVmV`
31	`LSU`	`mmVVVmmmVVVVmmmVV`
32	`LSZ`	`mVVmVmmVVmVVmVmmV`
33	`LZL`	`mmVVmVVmmVV`
34	`LZS`	`VmmVmVVmVVmmVmVVm`
35	`LZU`	`mmmVVVmmVVVmmmVVV`
36	`SJL`	`VVmVVmmmVVm`
37	`SLU`	`mmVVVVmmmVVmmmVVV`
38	`SLZ`	`mVVmVVmVmmVmmVVmV`
39	`SSU`	`VVVmmmVVVmmVVVmmmmVVVmmmVV`
40	`SUJ`	`mVVVmVVmmmVmmVVVm`
41	`SUS`	`VmVVmVVmVVmmVmmVmmVmVVmVVm`
42	`SZZ`	`mVmmVVmVVmVmmVVmVmmVmmVVmV`
43	`UJJ`	`VmmVVVmVVmm`
44	`ULU`	`mmmVVVmmVVVVmmmVV`
45	`ULZ`	`mVmmVVmVVmVVmVmmV`
46	`UUU`	`VVmmmmVVVmmVVVVmmVVVmmmmVV`
47	`ZJU`	`VVVmmmVVmmmVVVVmm`
48	`ZLS`	`VmVVmmVmmVmVVmVVm`
49	`ZSJ`	`VVmmVmmVVmmVVVmmV`
50	`ZUJ`	`mVVVmmVmmmVVmVVVm`
51	`JJLJ`	`mVVVmmVVmVVmmmV`
52	`JLJJ`	`VmmVVVmVVmmmVVm`
53	`JLJL`	`VmmVVVmVVmmmVVm`
54	`LJJL`	`VVmmVmmVVVmVVmm`
55	`LLJJ`	`VmmmVVmVVmmVVVm`
56	`SZUS`	`VmVVmVVmmVmmVmmVmVVmVVmVVmVVmmVmmVmmVmVVmVVmVVmmVmmVmmVmVVmVVmmVmmVmmVmVVmVVmVVm`
57	`ULLS`	`VmmVmmVmVVmVVmmVmVVmVVmVVmmVmmVmVVm`
58	`JJJJZJ`	`VmmVVVmmVVmVVmmVVmmmVVmVVmmVVVmmVVmmVmmVVmmmVVmVVmmVVVmmVVmVVmmVVmmmVVmmVmmVVVmmVVmmVmmVVmmmVVm`
59	`JULLLJ`	`mmVmmVVmmmVVmVVVmmVmmVVVmmVVmVVVmmVmmVVmmmVVmVVVmmVmmVVVmmVVmVVmmmVmmVVmmmVVmVVmmmVmmVVVmmVVmVV`
60	`LJJJUL`	`mVVVmVVmmmVVmVVVmmVmmmVmmVVVmVVmmmVmmVVVmmVmmmVVmVVVmVVmmmVVmVVVmmVmmmVVmVVVmVVmmmVmmVVVmmVmmmV`
61	`LJSJJL`	`VVmVVmmVVVmmVmmmVVmVVmmmVVmmVmmVVVmVVmmmVVmmVmmVVVmVVmmVVVmmVmmmVVmVVmmVVVmmVmmVVVmVVmmmVVmmVmm`
62	`LZLLLJ`	`mmVmmVVmmmVVmVVmmmVmmVVVmmVVmVVVmmVmmVVmmmVVmVVVmmVmmVVVmmVVmVVmmmVmmVVmmmVVmVVVmmVmmVVVmmVVmVV`
63	`SJJJJL`	`VVmVVmmVVVmmVmmVVVmVVmmmVVmmVmmVVVmVVmmVVVmmVmmmVVmVVmmmVVmmVmmmVVmVVmmVVVmmVmmVVVmVVmmmVVmmVmm`
64	`ZLJLJL`	`VmmVVVmmVmmmVVmVVmmVVVmVVmmmVVmmVmmVVVmmVmmmVVmmVmmVVVmVVmmmVVmVVmmVVVmmVmmmVVmVVmmVVVmVVmmmVVm`

C/C++/Java 用のテストデータ

/*0*/ test( "JZ", "mVVmV" );    
/*1*/ test( "J", "V" );    
/*2*/ test( "L", "V" );    
/*3*/ test( "Z", "mV" );    
/*4*/ test( "U", "VV" );    
/*5*/ test( "S", "Vm" );    
/*6*/ test( "JL", "VVm" );    
/*7*/ test( "JS", "VmVVm" );    
/*8*/ test( "JU", "VVVmm" );    
/*9*/ test( "LU", "mmVVV" );    
/*10*/ test( "SL", "VVmmV" );    
/*11*/ test( "SS", "VmVVmmVm" );    
/*12*/ test( "SU", "VVVmmmVV" );    
/*13*/ test( "SZ", "mVVmVmmV" );    
/*14*/ test( "UL", "mVVVm" );    
/*15*/ test( "UU", "mmVVVVmm" );    
/*16*/ test( "UZ", "mVVmVVmV" );    
/*17*/ test( "ZJ", "VmmVV" );    
/*18*/ test( "ZS", "VmmVmVVm" );    
/*19*/ test( "ZZ", "mVmmVVmV" );    
/*20*/ test( "JJJ", "VVmVVmm" );    
/*21*/ test( "JJZ", "mVVmVVmVmmV" );    
/*22*/ test( "JSJ", "VVmmVVmVVmm" );    
/*23*/ test( "JSS", "VmVVmmVmVVmVVmmVm" );    
/*24*/ test( "JUS", "VmVVmVVmVVmmVmmVm" );    
/*25*/ test( "JUU", "mmVVVVmmVVVmmmmVV" );    
/*26*/ test( "JUZ", "mVVmVVmVVmVmmVmmV" );    
/*27*/ test( "LJJ", "VmmVVVm" );    
/*28*/ test( "LLS", "VmmVmVVmVVm" );    
/*29*/ test( "LLU", "mmmVVVmmVVV" );    
/*30*/ test( "LLZ", "mVmmVVmVVmV" );    
/*31*/ test( "LSU", "mmVVVmmmVVVVmmmVV" );    
/*32*/ test( "LSZ", "mVVmVmmVVmVVmVmmV" );    
/*33*/ test( "LZL", "mmVVmVVmmVV" );    
/*34*/ test( "LZS", "VmmVmVVmVVmmVmVVm" );    
/*35*/ test( "LZU", "mmmVVVmmVVVmmmVVV" );    
/*36*/ test( "SJL", "VVmVVmmmVVm" );    
/*37*/ test( "SLU", "mmVVVVmmmVVmmmVVV" );    
/*38*/ test( "SLZ", "mVVmVVmVmmVmmVVmV" );    
/*39*/ test( "SSU", "VVVmmmVVVmmVVVmmmmVVVmmmVV" );    
/*40*/ test( "SUJ", "mVVVmVVmmmVmmVVVm" );    
/*41*/ test( "SUS", "VmVVmVVmVVmmVmmVmmVmVVmVVm" );    
/*42*/ test( "SZZ", "mVmmVVmVVmVmmVVmVmmVmmVVmV" );    
/*43*/ test( "UJJ", "VmmVVVmVVmm" );    
/*44*/ test( "ULU", "mmmVVVmmVVVVmmmVV" );    
/*45*/ test( "ULZ", "mVmmVVmVVmVVmVmmV" );    
/*46*/ test( "UUU", "VVmmmmVVVmmVVVVmmVVVmmmmVV" );    
/*47*/ test( "ZJU", "VVVmmmVVmmmVVVVmm" );    
/*48*/ test( "ZLS", "VmVVmmVmmVmVVmVVm" );    
/*49*/ test( "ZSJ", "VVmmVmmVVmmVVVmmV" );    
/*50*/ test( "ZUJ", "mVVVmmVmmmVVmVVVm" );    
/*51*/ test( "JJLJ", "mVVVmmVVmVVmmmV" );    
/*52*/ test( "JLJJ", "VmmVVVmVVmmmVVm" );    
/*53*/ test( "JLJL", "VmmVVVmVVmmmVVm" );    
/*54*/ test( "LJJL", "VVmmVmmVVVmVVmm" );    
/*55*/ test( "LLJJ", "VmmmVVmVVmmVVVm" );    
/*56*/ test( "SZUS", "VmVVmVVmmVmmVmmVmVVmVVmVVmVVmmVmmVmmVmVVmVVmVVmmVmmVmmVmVVmVVmmVmmVmmVmVVmVVmVVm" );    
/*57*/ test( "ULLS", "VmmVmmVmVVmVVmmVmVVmVVmVVmmVmmVmVVm" );    
/*58*/ test( "JJJJZJ", "VmmVVVmmVVmVVmmVVmmmVVmVVmmVVVmmVVmmVmmVVmmmVVmVVmmVVVmmVVmVVmmVVmmmVVmmVmmVVVmmVVmmVmmVVmmmVVm" );    
/*59*/ test( "JULLLJ", "mmVmmVVmmmVVmVVVmmVmmVVVmmVVmVVVmmVmmVVmmmVVmVVVmmVmmVVVmmVVmVVmmmVmmVVmmmVVmVVmmmVmmVVVmmVVmVV" );    
/*60*/ test( "LJJJUL", "mVVVmVVmmmVVmVVVmmVmmmVmmVVVmVVmmmVmmVVVmmVmmmVVmVVVmVVmmmVVmVVVmmVmmmVVmVVVmVVmmmVmmVVVmmVmmmV" );    
/*61*/ test( "LJSJJL", "VVmVVmmVVVmmVmmmVVmVVmmmVVmmVmmVVVmVVmmmVVmmVmmVVVmVVmmVVVmmVmmmVVmVVmmVVVmmVmmVVVmVVmmmVVmmVmm" );    
/*62*/ test( "LZLLLJ", "mmVmmVVmmmVVmVVmmmVmmVVVmmVVmVVVmmVmmVVmmmVVmVVVmmVmmVVVmmVVmVVmmmVmmVVmmmVVmVVVmmVmmVVVmmVVmVV" );    
/*63*/ test( "SJJJJL", "VVmVVmmVVVmmVmmVVVmVVmmmVVmmVmmVVVmVVmmVVVmmVmmmVVmVVmmmVVmmVmmmVVmVVmmVVVmmVmmVVVmVVmmmVVmmVmm" );    
/*64*/ test( "ZLJLJL", "VmmVVVmmVmmmVVmVVmmVVVmVVmmmVVmmVmmVVVmmVmmmVVmmVmmVVVmVVmmmVVmVVmmVVVmmVmmmVVmVVmmVVVmVVmmmVVm" );

山折り谷折り〜 横へな 2014.2.1 参考問題

問題

入力と出力

補足

サンプルデータ

C/C++/Java 用のテストデータ

山折り谷折り〜横へな 2014.2.1 参考問題