TopCoder Statistics - Problem Statement

Problem Statement

We have decided to make a funnier programming language, and name it "Tribblo". The basic objects of the new programming language will be tiny two dimensional creatures called Tribbles. The way tribbles interact with their world will determine the flow of a program. For starters, only 5 objects that tribbles can interact with are defined.

'S' represents a spawning point. The program starts by summoning one tribble at this point. The tribble then begins moving in one of the four cardinal directions (up, down, left or right). The direction is chosen randomly and each direction has the same chance of being chosen (25%). If at any point during the program the tribble returns to the spawning point the tribble is destroyed causing the program to enter an infinite loop and never terminate.
A slash-router '/' (quotes for clarity) works like a mirror. When a tribble hits a slash-router, it will rotate 90 degrees and continue moving. If the tribble was originally moving left or right, it will rotate 90 degrees counterclockwise, and if it was originally moving up or down, it will rotate 90 degrees clockwise.
A backslash-router '\' (quotes for clarity) works similarly to the slash-router, but in the opposite direction. If the tribble was originally moving left or right, it will rotate 90 degrees clockwise, and if it was originally moving up or down, it will rotate 90 degrees counterclockwise.
For example if the code looks like this:
```
		...\..
		......
		S../..
```
a tribble that starts off going to the right moves like this:
```
		ttt\..
		...t..
		Stt/..
```
There is also a wherever machine 'W'. When a tribble hits this object, it will rotate 90 degrees either clockwise or counterclockwise (both possibilities are equally likely). For example, a tribble going left and hitting the machine has a 50% chance of going up and a 50% chance of going down. There will be at most 10 wherever machines.
The final object is the tribble-trouble object 'T'. If any tribble reaches a tribble-trouble object, the program terminates.

The tribblo world is a N*M matrix of characters, with empty squares represented as '.'. If a tribble exits the boundaries of the world, he falls off, causing the program to enter an infinite loop and never terminate. You will be given a String[] code containing a properly formatted Tribblo program. You need to determine the probability of the given Tribblo program terminating.

Definition

Class:: TribbloTrouble
Method:: terminates
Parameters:: String[]
Returns:: double
Method signature:: double terminates(String[] code)
(be sure your method is public)

Notes

The returned value must be accurate to within a relative or absolute value of 1E-9.

Constraints

code will contain between 1 and 50 elements, inclusive.
Each element of code will contain between 1 and 50 characters, inclusive.
All elements of code will contain the same number of characters.
All elements of code will contain only 'S','T','/','\','W' or '.' characters.
There will be at most 10 'W' characters in code.
There will be exactly one 'S' character in code.

Examples

{"..T..", "T.S.T", "..T.."}

Returns: 1.0

Whatever the initial direction of the tribble is, he is bound to enter a tribble-trouble. Therefore, the program will always terminate.
{".....", "T.S.T", "....."}

Returns: 0.5

If the tribble starts off moving left or right, the program will terminate. However, if it starts off moving up or down, it will fall off an edge and the program will enter an infinite loop. Therefore, out of 4 equally probable starting directions, 2 will terminate the program.
{"./..T", ".\\..\\", "S.../"}

Returns: 0.25

A tribble that starts off moving to the right will rebound a bit around the routers and end up hitting the tribble-trouble. Any other starting direction will cause the tribble to fall off the board (please note that '\\' represents a single '\' character!)
{"...W..T", ".......", "...S..."}

Returns: 0.125

The famous wherever object! The tribble has a 25% chance of initially going upwards. When it hits the wherever machine it has a 50% chance of going to the left and falling off and a 50% chance of going to the right and terminating the program. 25% * 50% = 12.5%
{"..../T....T...T..", "/..W.W.....T.....", "....W...S.W......", "................."}

Returns: 0.25
{"/..\\", "S../"}

Returns: 0.0

Be careful! If the tribble returns to the spawning point it is destroyed, and the program will enter an infinite loop.
{"..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................../.........\\....................", "..................................................", "................/..W..............................", "..................................................", "............./..W..W..\\...........................", "..................................................", "..........S..W..W..W..W......T....................", "..................................................", ".............\\..W..W../...........................", "..................................................", "................\\..W..............................", "..................................................", "...................\\........./....................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................................................."}

Returns: 0.24999999999999986
{"..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "......................T.T.........................", "......................WWW.........................", "......................T.T.........................", "..................................................", "...................TWT............................", "....................W..S...W......................", "...................TWT............................", "..................................................", "..................................................", "......................WWW.........................", "......................T.T.........................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................................................."}

Returns: 0.75
{"..................................................", "..................................................", "..................................................", "......................................./..........", "............................T.....................", "........./....../...................../...........", "..................................................", "................................../...............", ".............../..................................", "..................................................", ".............................TTTTT................", "...........TT.....................................", "..................................................", "......../.........................................", "..................................................", ".............................T....................", "................/......................./.........", "..................................................", ".............../....../.T.........................", "......................WWW.........................", "............../.......T./..............\\..........", "..................................................", "...................TWT...../.........../..........", "....................W..S...W......................", "........./..........WT.....T......................", "..................................................", "......................T.T.........................", "...............T......WWW.........................", "......................T.T.........................", "...............T..................................", ".................T................/../............", "..............T...................................", "..................................................", "..................................................", ".........\\............./..........................", "..................................................", "..................................................", ".............../....../...........................", "..................................................", ".............................T....................", "...................................../............", "......../.........................................", "..................................................", ".............T......../.......T...................", "..................................................", "................/.................................", "...............................T..................", "..................................................", "..................................................", ".................................................."}

Returns: 1.0
{"..................................................", "..................................................", "......................................T...........", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................................W..../...........", "..................................................", "..................................................", "..................................................", ".............................W...W................", "..................................................", "..................................................", "........................W....W....................", "..................................................", "..................................................", "..................................................", "..................................................", "...................W....W.........................", "..................................................", "..................................................", "..................................................", "..............W....W..............................", "..................................................", "..................................................", ".........S....W...................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................................................."}

Returns: 2.44140625E-4
{"S"}

Returns: 0.0
{".....", "./..\\", "SW...", ".\\../"}

Returns: 0.0
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Returns: 0.25
{"/................................................\\", "./..............................................\\.", "../............................................\\..", ".../..........................................\\...", "..../........................................\\....", "...../......................................\\.....", "....../....................................\\......", "......./..................................\\.......", "......../................................\\........", "........./..............................\\.........", "........../.............W..............\\..........", ".........../...........W..............\\...........", "............/........................\\............", "............./......................\\.............", "............../....................\\..............", ".............../..................\\...............", "................/................\\................", "................./..............\\.................", "................../............\\..................", ".................../..........\\...................", "..................../........\\....................", "...................../......\\.....................", "....................../....\\......................", "......................./..\\.......................", "........................T\\......................WW", ".......................\\./......................WW", "......................\\.../.......................", ".....................\\...../......................", "....................\\......./.....................", "...................\\........./....................", "..................\\.........../...................", ".................\\............./..................", "................\\.............../.................", "...............\\................./................", "..............\\.................../...............", ".............\\...................../..............", "............\\......................./.............", "...........\\........................./............", "..........\\.........................../...........", ".........\\............................./..........", "........\\.............................../.........", ".......\\................................./........", "......\\.................................../.......", ".....\\...................................../......", "....\\......................................./.....", "...\\........................................./....", "..\\.........................................../...", ".\\............................................./..", "\\.......................W..W..................../.", "S.......................W..W...................../"}

Returns: 0.010259037109956275
{"..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "...................../..\\.........................", "..................................................", "..................................................", "................./...S../.........................", "..................................................", "..................................................", ".................\\...W..T.........................", "..................................................", "..................................................", "................./...W..T.........................", "..................................................", ".................\\...W............................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................................................."}

Returns: 0.20833333333333331
{"..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "................/.................................", "..................................................", "..................................................", "..................................................", "...............................T..................", "..................................................", "......................T...........................", "..................................................", "...............W..................................", "...............T..................................", "..............TWT.................................", "......./.......SW..T..W........W..................", "................T.................................", "..................................................", "............................................W.....", ".......\\.......W...W../........W...........W......", "..................................................", "..................................................", ".............................../..................", "..................................................", "...............\\.T./..............................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................................................."}

Returns: 0.75
{"T.../............/..../\\.../..../../..\\...//\\..../", "\\...\\.........../.T.../......./.\\......./...../...", "../....W.\\.\\//\\../\\..././.............././......\\.", "\\..\\/\\..//../../..\\.T.....\\.....//..W........./.\\.", "./.....T./../..../.../........\\..../...WS\\/\\...\\..", "./...\\//......\\......//../...\\....\\.../..../......", "/............\\/..\\..//................../....../..", ".......//\\../........\\.......T\\\\/........../.\\/.\\.", "/....//.../........\\..../\\.\\......T\\./..\\....\\\\...", "/.T\\.\\.\\\\../........\\......\\...../../...\\..\\W/.\\/\\", "./........\\.......././....\\W../\\........./..../...", ".\\.\\.\\//././....\\.....T...\\...........././..\\.....", "..\\./.....\\../..\\././.......\\.\\......\\......./\\.//", "...\\..../\\\\\\\\......\\\\..../\\.....\\.....\\/....//..\\.", ".\\/\\...\\........../.../...W..\\..../........\\/.....", "\\............/....\\\\..T.\\\\T......./.\\\\../.\\.....\\/", "/.......\\.\\\\././.../.\\...\\/...\\/..\\....\\...../.W.\\", "........\\.../..../........../\\\\../\\.\\...../..../..", ".\\../..\\......./.....\\./....\\.../T.\\\\.....\\\\./....", "./.....\\./.../.../..T.............\\\\/...\\......\\.\\", "../.........../\\./.../....\\...\\/....../../...\\../.", "........\\..././\\./../.\\..//././.././..\\././.......", "....\\...\\./.....\\/\\./...........\\.\\.T../T/.....//.", "\\...\\./.....\\..../......T...../\\..................", ".\\../\\/../...\\..././\\/....\\\\....\\\\..\\..........\\..", "..\\......\\./....\\../.\\.....\\.\\.\\.././\\..\\.........", ".\\../../...\\../\\..../..\\..W..............\\.../....", "..\\../..../..\\.....\\\\\\.\\.../.\\../....\\......../../", "..../..\\..../....../.......\\.T..\\....../....\\\\....", "......\\..\\.../.T\\.../........./.............\\./\\..", ".\\\\/../..\\../...............\\\\\\./..\\.....\\........", ".\\........T....W/\\...../..//..T/\\\\././..\\..\\/...\\.", "..../...../.......././......./.....\\\\./........\\..", "../\\.\\.T..\\.\\......./.........\\./\\..../../..T.\\...", ".....\\.T....//\\......./..././\\\\...\\..../..\\/......", "\\.../.T.../.../.\\...//T.../...\\/../.\\..\\.T\\/../...", "....................T.../....\\.....\\..\\........\\..", "../..\\\\\\....\\\\.........../.../\\......\\../.\\....../", "...\\....../..........\\........../......\\/./...\\./.", "./...\\../...../\\......./......../..\\./...\\.....\\..", "/...\\.........../.....\\..................../.\\...\\", "..\\.......\\..../..../....///..../\\/.....\\\\........", "\\\\/.\\..../....\\......\\.\\.............\\/.../.\\....\\", ".\\/\\...././/\\.\\..\\..\\../\\../.\\./..\\/..\\...\\....../", "........./..........\\........../............./../.", "T..........\\/.../.\\../...\\..\\......\\....../\\.....\\", "...\\../..../.\\......./../........../......\\.W/../.", "/..\\/\\....../..\\T....../\\\\../../.../...\\.T....//.\\", "/\\......./.\\./.T..../\\/..\\./.../......\\.\\.\\.../..\\", "\\......\\.....\\\\.../........../\\../.\\..\\...../..\\.."}

Returns: 0.375
{"/./.\\..\\.../.....//...\\.\\....//../\\//..\\....../\\\\\\", "/\\\\................../.\\...../\\\\../\\../.\\..\\\\./.\\\\", "......\\.../.\\/.../\\./...\\...\\.........././.\\.\\....", "..\\\\.....\\\\....\\..T..\\././.\\\\/\\.\\./......\\....../.", "......../W...\\./..../......\\.\\./.\\\\./........../.\\", "..../...././\\./...............W.....\\.\\../.../.\\..", "........../..\\..../.\\/..///\\......./\\/............", "\\./..\\./.....//..././../..../..\\..\\.../...........", "....///./\\\\./.\\./....../\\...\\./..././\\/../...//../", ".../..........\\.//..../..\\\\//.../....\\/..\\/\\\\....\\", "...../.\\.\\............/.\\./.\\.//.....\\.\\.\\..\\.....", "..\\\\.........\\......\\.../../......W../\\...../.....", "./.\\.\\.\\./...\\..../...\\\\//./..././....././..\\\\/...", ".\\/.............\\..\\.\\..//.......\\..........\\/\\...", "...\\/\\././..\\...\\...././/\\..././/........\\/..../..", "/...//\\.........\\.........\\..........\\....../.././", "....../.....\\...\\./.W......\\.\\....\\.........\\.....", "/.../\\\\..W\\...\\./.SW/\\.........../...\\..\\.../.....", "......../\\\\.//.......\\....\\......./..\\..\\/...\\..\\.", "\\.........../\\\\/\\....../././.\\......./..\\...././..", "...\\/......./..W.....\\...\\....................../.", "./../.../.........//./../...../\\.../\\.\\..\\........", "/...../.\\............/../........\\\\...\\...../\\...\\", "....../..\\/../...\\/./..\\...\\....../\\./..../...\\../", "....//..../.....\\........\\\\..........\\.........\\..", "....\\........\\.../\\.W.\\..\\\\.\\\\.../../...\\.....\\/..", "...........\\......../.\\.................\\.........", "/.........\\............./...\\........\\........\\...", ".......................\\........./..../....../....", "...................\\..\\./....././/.........\\\\../..", "...../W/\\../.\\\\\\.\\..........\\..\\///....\\......\\...", "...../....../.....././......//\\./......./.........", "..\\.../.\\../.....\\.\\./......./....\\...\\./..../....", "..///................/..\\\\....../\\......\\...\\T....", ".....\\/...\\.../........././\\\\.....\\...........\\...", "./.\\...\\......\\......../../....//...\\........\\/..\\", "/.....\\...\\/......\\.....\\.\\\\\\......../...\\......\\.", "\\...\\.\\/./.......\\//../...........\\....\\....\\....\\", "..........\\....//.../\\.\\..../\\...../........./..\\/", "\\.......\\..........\\.\\.......\\.....\\....\\./\\\\./...", "../..\\......./.././...//.../..../........../.\\\\...", ".\\.\\.......\\.....\\..../..../..../\\....W\\./.....\\..", "\\\\./.\\..\\.\\/\\....../\\/..\\................../..\\./.", "......../../................//.../.\\../.....\\.\\...", ".....././......\\.../..\\...\\..../...\\./.\\..........", "..\\....../....\\/...\\......../../....../../......\\\\", "/../.......\\...\\....\\\\.............../.\\/..../.\\.\\", "/.../....\\....\\/...T....\\/./.../..............\\/..", "/........\\/..\\../\\./.\\./....../........\\......../.", "..........\\\\...../..\\/\\...\\//...../....\\..../\\...."}

Returns: 0.4375
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Returns: 0.125
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Returns: 0.375
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Returns: 0.6875
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Returns: 0.5
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Returns: 0.5625
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Returns: 0.375
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Returns: 0.125
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Returns: 0.375
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Returns: 0.625
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Returns: 0.5
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Returns: 0.125
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Returns: 0.625
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Returns: 0.9375
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Returns: 0.4375
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Returns: 0.375
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Returns: 0.8125
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Returns: 0.59375
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Returns: 0.375
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Returns: 0.06666666666666667
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Returns: 0.08333333333333333
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Returns: 0.08333333333333333
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Returns: 0.5833333333333333
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Returns: 0.25
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Returns: 0.03571428571428571
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Returns: 0.16666666666666666
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Returns: 0.375
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Returns: 0.0
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Returns: 0.0013020833333333333
{ "/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\T.", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "S/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/" }

Returns: 0.25
{ "/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/S", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\W\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "T/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/" }

Returns: 0.25
{ "/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/S", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\W\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "//////////////////////////////////////////////", "\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\", "T/\\/\\/\\/\\/\\/\\W\\W\\W\\W\\W\\W\\W\\W\\W\\/\\/\\/\\/\\/\\/\\/\\/" }

Returns: 4.8828125E-4
{"W/WT", "SWW/" }

Returns: 0.03571428571428571
{"SWWW", "WWWW", "WWTW" }

Returns: 0.07655502392344497
{"\\///\\\\////\\////..................................", ".................................................", ".................................................", ".................................................", ".........................///\\/\\/\\/\\/\\/\\\\/\\///\\...", ".................................................", ".................................................", ".................................................", ".................................................", ".................................................", "..../////////////////////////////................", ".................................................", ".................................................", ".................................................", ".................................................", ".................................................", ".................................................", ".................................................", ".................................................", ".................................................", "..........W......\\...............................", ".................................................", ".................................................", ".................................................", ".................................................", "..........\\......W.........W.....................", ".................................................", ".................................................", ".................................................", ".................S...............................", "...................................W.............", ".................................................", ".................................................", ".................................................", ".................\\\\........W.......W.............", "..................\\\\.............................", ".................................................", ".................................................", ".................................................", "..........W......W./.......W.....................", ".............................................\\...", ".............................................\\...", ".\\/\\.........................................\\...", ".\\T\\...............................W.......T.\\...", ".\\\\\\.........................................\\...", "................/\\/\\/\\/\\//\\/////\\/////\\///\\/\\/...", ".................................................", ".\\\\\\\\\\\\\\\\\\.......................................", ".................................................", "................................................." }

Returns: 0.020833333333333332
{"WWT", "WWW", "WWW", "SWW", ".\\/" }

Returns: 0.035460992907801414
{"..................................................", "..................................................", "....T........./..........\\........................", "..................................................", "......./.................W.....W...............T..", "..................................................", "..................................................", "..................................................", "....W..W.................W.....W...............T..", "..................................................", "..................................................", "..................................................", "..................................................", "....W..W......S................W..................", "..................................................", "..................................................", "..................................................", "..................................................", "....T..W....../...................................", "..............T................/.................." }

Returns: 0.4294041450777202
{"S..............................................WWW", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "\\.............................................\\...", "/............................................./...", "W..............................................WWW", "W..............................................WWT" }

Returns: 0.031088082901554404
{"TT..T", "TWWW.", "TWWW.", "TWWW.", "S/..." }

Returns: 0.3958333333333333
{"T...W....W..", "............", ".W.......W..", "............", ".W.......W..", "............", ".W..W....W.T", "............", "............", "............", "............", "\\S.W...../.." }

Returns: 0.28190376569037656
{"TTTTT.", "WWWWWT", "SWWWWT" }

Returns: 0.14533492822966507
{"/.\\...", "......", "\\.W.T.", "......", "./S\\.." }

Returns: 0.25
{"/W.", "\\WT", "TST", ".T." }

Returns: 0.9166666666666666
{"/\\.\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\.......................S..W.W.W.W.W.W.W.W.W.W.../", "/................................................\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\............................T.................../", "/................................................\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\................................................/", "/................................................\\", "\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/" }

Returns: 0.15277777777777585
{"WWWWWS", "WWWWWT" }

Returns: 0.31698717948717947
{".............////////////////////////.............", "..................................................", ".....\\\\\\\\\\\\\\\\\\\\\\.....T.........T..........\\\\\\\\....", "...........T............\\\\\\\\\\\\\\\\\\\\\\...............", "....\\\\\\\\..........................................", "............T..../........T.....T......T..........", ".......T..........................................", "...................W..............................", "...........................T.....T...../..........", ".....T............................................", "............W...../.......W..../.......\\\\\\\\.......", "..................................................", "...\\\\\\\\\\...............T...........W..............", "...........W......................................", "...../...............................//////.......", "................\\\\\\\\......S....................T..", "..................................................", ".....//////...........W...W.......T...............", "..T......W..............................T.........", "..................................................", "....../............/....\\\\\\\\\\........./...........", "...............W..................................", "...T..............................................", "......T.........T..........T.......T..............", "..T..../....../...................................", ".....//........T............T.....................", "...../...................................T........", "........................T...........W.............", "..../........................\\\\\\\\\\\\...............", "........T..........///////////////////............", "...............................././...............", "...\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\.......................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".................................................." }

Returns: 0.5
{"...T..", "/S.W.\\", "\\\\.W./" }

Returns: 0.16666666666666666
{".WW.", "SWWT" }

Returns: 0.016666666666666666
{"...T.", "TW.WT", ".....", "TW.W.", ".S.T." }

Returns: 0.4833333333333333
{"./\\", "TW/", ".S." }

Returns: 0.25
{".W.W.T", "WWSWW.", "W...W." }

Returns: 0.06274509803921569
{"W.W.W.W", "W..S..W", "W.W.W.W" }

Returns: 0.0
{"WW", "WS", "WT" }

Returns: 0.3125
{"TW..W.T.W.", "..........", "..........", ".T........", ".W..W...W.", ".......T..", "..........", ".W\\.W...W.", "\\\\\\.S.....", ".T/.W.../." }

Returns: 0.17500000000000002
{"/...............................................\\.", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\..............................................\\..", "/............................................../..", "\\...............................................WT", "..................................................", "S.............................................../." }

Returns: 0.25
{"./\\", "TW/", "...", "...", ".S." }

Returns: 0.25
{".T.", "/W\\", "\\W/", ".S." }

Returns: 0.25
{"/..............................W.................T", "\\..............................W.................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................\\", "/................................................/", "\\................................................S" }

Returns: 0.08333333333333333
{".T.T.", "TWWWT", "SWWWW", "TWWWT", ".T.T." }

Returns: 0.6666666666666665
{"/W/", "\\WT", "/S\\" }

Returns: 0.16666666666666666
{"..S", ".WW", "TWW" }

Returns: 0.03333333333333333
{"WWW", "WSW", "WWW", "WWT" }

Returns: 0.1
{"TTTTT", "TWWST", "TWW.T", "TTTTT" }

Returns: 1.0
{"/\\/\\..", "\\WWW\\.", "/WSW.\\", "\\WWWT.", ".\\/\\./" }

Returns: 0.3363715277777777
{"TT/..............................................\\", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "\\SW............................................../", ".T................................................" }

Returns: 0.75
{"./\\/\\/\\/\\/\\/\\/\\/\\/\\/\\.", "/....................\\", "\\..........T........./", "/....................\\", "\\.........W........../", "/.......W..W.........\\", "\\.....W............../", "/.................T..\\", "\\..................../", "/.............T......\\", "\\..................../", "/...........S....W...\\", "\\.....WW..W........../", "/.......T............\\", "\\..................../", "/....................\\", "\\........W.........../", "/...........W..T.....\\", "\\..................../", ".\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/." }

Returns: 0.9974489795918366
{"...../\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\.", "..................................................", "..................................................", "..................................................", ".S...W........................................../.", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", "..................................................", ".....T\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/\\/.." }

Returns: 0.25

Statistics

Problem Statement for "TribbloTrouble"

Problem Statement

Definition

Notes

Constraints

Examples