Statistics

Problem Statement

NOTE: This problem statement contains an image that may not display properly if viewed outside of the applet.

You will be given the map of a maze, with exactly two openings on the boundary. Your task is to add mirrors to the maze in such an arrangement that if a laser is shined through one opening in the boundary, it will exit through the other opening. Your method should return the least number of mirrors necessary to be added in order to accomplish this. If no solution is possible, return -1.

The maze will consist of walls ('#'), open spaces ('.'), and mirrors ('/' and '`') arranged on a regular grid. The laser may only travel though open spaces and reflect off of mirrors. If it hits a wall, the light will be absorbed. You may only place mirrors on open spaces.

Mirrors are always at a 45-degree angle to the axes of the maze, and deflect the laser at a right angle.

For example, given the following maze:

    #######
    ##....#
    ##.##.#
    ##.##.#
    ......#
    ##.####
    ##.####

There are three arrangements of mirrors that will deflect the laser from one opening in the boundary to the other:

These three solutions require 1, 3, and 4 mirrors, respectively. The least number of mirrors needed is 1, so 1 is the correct answer.

The map may have mirrors already placed, which you may use but cannot move. For example, given the following map:

    #######
    ##....#
    ##.##.#
    ##.##.#
    ../...#
    ##.####
    ##.####

there is only one solution (the third arrangement in the figure above). Three more mirrors must be added, so the correct answer in this case is 3.

Definition

Class:

MirrorPlacement

Method:

mirrors

Parameters:

String[]

Returns:

int

Method signature:

int mirrors(String[] map)

(be sure your method is public)

Notes

• Since '\' is a special character, we will use the '/' (forward slash) and '`' (back quote) characters to indicate mirrors in the input.

Constraints

• map will contain between 3 and 50 elements, inclusive.
• The length of each element of map will be the same, and be between 3 and 50, inclusive.
• map will contain only the characters '#', '.', '/', and '`'.
• Exactly 2 characters on the boundary of map will be '.'. All other characters on the boundary will be '#'.
• The characters in the four corners of map will be '#'.

Examples

1. { "#######", "##....#", "##.##.#", "##.##.#", "......#", "##.####", "##.####" }

   Returns: 1

   This is the first example in the problem statement.

2. { "########", "##....##", "##.##.##", "##...`..", "#####.##" }

   Returns: 3

   This is similar to the second example in the problem statement.

3. { "##################################################", "#................................................#", ".................................................#", "#................................................#", "#.................................................", "#................................................#", "##################################################" }

   Returns: 2

   There are many 2-mirror solutions possible, all with '`' mirrors in the same column of the 3rd and 5th rows.

4. { "########", "##....##", "##.##.##", "##.../..", "#####.##" }

   Returns: 0

5. { "###########", "...../.....", "#####.#####", "###.....###", "###.###.###", "###.....###", "###########" }

   Returns: -1

   No solution is possible.

6. { "########.##", "#.......`.#", "#.......#.#", "#..#...#./#", "#//#....`.#", "#...#.....#", "###.#######" }

   Returns: 9

7. { "########.##", "#./......`#", "#../.`....#", "#.`...../.#", "#....`.../#", "###.#######" }

   Returns: 0

8. { "##################################################", "#..............................................#.#", "...............................................#.#", "#..............................................#.#", "#................................................#", "#..............................................#.#", "################################################.#", "#.#............................................#.#", "#..............................................#.#", "#.#............................................#.#", "#.#..............................................#", "#.#............................................#.#", "#.################################################", "#.#..............................................#", "#................................................#", "#.#..............................................#", "#.#...............................................", "#.#..............................................#", "##################################################" }

   Returns: 10

9. { "#.#####", "#..####", "##..###", "###..##", "####..#", "#####.#" }

   Returns: 8

10. { "###", "#..", "#.#" }

    Returns: 1

11. { "####", "####", "#..#" }

    Returns: 2

12. { "########.##", "#.........#", "#/.........", "#.........#", "#`....../.#", "###########" }

    Returns: 0

13. { "##################################################", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#############################################..###" }

    Returns: 2

14. { "##################################################", ".................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "#................................................#", "################################################.#" }

    Returns: 1

15. { "##################################################", ".`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`.#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "################################################.#" }

    Returns: 0

16. { "##################################################", ".`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`.#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/``#", "#//`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/#", "#`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`/`.#", "################################################.#" }

    Returns: 1

17. { "#.#", "##.", "###" }

    Returns: -1

18. { "#.#", "#..", "###" }

    Returns: 1

19. { "#.#", "#/.", "###" }

    Returns: -1

20. { "##################################################", "##################################################", "##################################################", "##################################################", "##################################################", "##################################################", "##################################################", "##################################################", "##################################################", "########################................##########", "########################.##############.##########", "########################.##############.##########", "########################.##############.##########", "########################.##############.##########", "########################.##############.##########", "########################.##############.##########", "########################.##############.##########", "########################.##############.##########", "########################.##############.##########", "########################........#######.##########", "########################.######.#######.##########", "########################.######.#######.##########", "########################.######.#######.##########", "#####...................`######.#######.##########", "########################.######.#######.##########", "########################.######.#######.##########", "########################........#######.##########", "########################.##############.##########", "########################.##############.##########", "####################.....##############.##########", "####################.###.##############.##########", "####################.###.##############.##########", "####################.###.##############.##########", "####################.###/......`............######", "####################.###.######.#######.##########", "####################.....######.#######.##########", "########################.######.#######.##########", "########################.######.#######.##########", "########################.######.#######.##########", "########################.######.#######.##########", "########################.######.#######.##########", ".........................######.#######.##########", "###############################.#######.##########", "###############################.#######.##########", "###############################.#######.##########", "###############################.#######.##########", "#######################################.##########", "#######################################.##########", "#######################################.##########", "#######################################.##########" }

    Returns: 11

21. { "##################################################", "#....###...###...###...###...###...###...###...###", "#.##..##.#..##.#..##.#..##.#..##.#..##.#..##.#..##", "#.###..#..#..#..#..#..#..#..#..#..#..#..#..#..#...", "#.####..#..#..#..#..#..#..#..#..#..#..#..#..#..###", "#.#...#..#..#..#..#..#..#..#..#..#..#..#..#..#..##", "#.#.#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#", "#.#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#.#", "#.##..#..#..#..#..#..#..#..#..#..#..#..#..#..#...#", "#.###..#..#..#..#..#..#..#..#..#..#..#..#..#..####", "#.####..#..#..#..#..#..#..#..#..#..#..#..#..#..###", "#.#...#..#..#..#..#..#..#..#..#..#..#..#..#..#..##", "#.#.#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#", "#.#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#.#", "#.##..#..#..#..#..#..#..#..#..#..#..#..#..#..#...#", "#.###..#..#..#..#..#..#..#..#..#..#..#..#..#..####", "#.####..#..#..#..#..#..#..#..#..#..#..#..#..#..###", "#.#...#..#..#..#..#..#..#..#..#..#..#..#..#..#..##", "#.#.#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#", "#.#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#.#", "#.##..#..#..#..#..#..#..#..#..#..#..#..#..#..#...#", "#.###..#..#..#..#..#..#..#..#..#..#..#..#..#..####", "#.####..#..#..#..#..#..#..#..#..#..#..#..#..#..###", "#.#...#..#..#..#..#..#..#..#..#..#..#..#..#..#..##", "#.#.#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#", "#.#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#.#", "#.##..#..#..#..#..#..#..#..#..#..#..#..#..#..#...#", "#.###..#..#..#..#..#..#..#..#..#..#..#..#..#..####", "#.####..#..#..#..#..#..#..#..#..#..#..#..#..#..###", "#.#...#..#..#..#..#..#..#..#..#..#..#..#..#..#..##", "#.#.#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#", "#.#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#.#", "#.##..#..#..#..#..#..#..#..#..#..#..#..#..#..#...#", "#.###..#..#..#..#..#..#..#..#..#..#..#..#..#..####", "#.####..#..#..#..#..#..#..#..#..#..#..#..#..#..###", "#.#...#..#..#..#..#..#..#..#..#..#..#..#..#..#..##", "#.#.#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#", "#.#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#.#", "#.##..#..#..#..#..#..#..#..#..#..#..#..#..#..#...#", "#.###..#..#..#..#..#..#..#..#..#..#..#..#..#..####", "#.####..#..#..#..#..#..#..#..#..#..#..#..#..#..###", "#.#...#..#..#..#..#..#..#..#..#..#..#..#..#..#..##", "#.#.#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#", "#.#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#.#", "#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#...#", "##..#..#..#..#..#..#..#..#..#..#..#..#..#..#..####", "###..#..#..#..#..#..#..#..#..#..#..#..#..#..#..###", "####..#.##..#.##..#.##..#.##..#.##..#.##..#.##..##", "#####...###...###...###...###...###...###...###..#", "################################################.#" }

    Returns: 1359

22. { "#.################################################", "#.......`#########################################", "#.######.#########################################", "#......#.#########################################", "#.####.#.#########################################", "#....#.#.#########################################", "#.##.#.#.#########################################", "#.##.#.#.#########################################", "#/................/###############################", "###########.#.#.##.###############################", "###########.#.#.##.###############################", "###########.#.#....###############################", "###########.#.####.###############################", "###########.#......###############################", "###########.######.###############################", "###########`.......###############################", "##################.###############################", "##################........########################", "##################.######.########################", "##################.....`#.########################", "##################.####.#.########################", "##################....#.#.########################", "##################.##.#.#.########################", "##################.##.#.#.########################", "##################/.............../###############", "###########################.#.#.##.###############", "###########################.#.#.##.###############", "###########################.#.#....###############", "###########################.#.####.###############", "###########################.#`.....###############", "###########################.######.###############", "###########################........###############", "##################################.###############", "##################################........########", "##################################.#.#.##.########", "##################################.#.#.##.########", "##################################.#.#`...########", "##################################.#.####.########", "##################################.#......########", "##################################.######.########", "##################################/............./#", "##########################################.#.#.#.#", "##########################################.#.#`..#", "##########################################.#.###.#", "##########################################.#.....#", "##########################################.#####.#", "##########################################.......#", "################################################.#", "################################################.#", "################################################.#" }

    Returns: 13

23. { "##################################################", "##..`...///.#.../`/.....``/``....`#`//.../.##`...#", "#.../`./``.`/.`/...`.`../`/`/.`/`//....`/`/`.`.`.#", "###//.##.`#../../.....#...#`.#`./`.`.#...../#`#.`#", "#.#`./.##../``.##..//..`././```.``./#./.#.`...`.`#", "#`./`./#`...``.../...`#./#/`#.`/./`...##..//..#..#", "#.`./...`.`.`././/..`.`/../.`...`#/.#.#`..`..`//.#", "#././##...##`/.#//.`/./...`/`.#`##``/.`../.`..#..#", "#.`.//..`..```../...#..`...#.../.#`/`......#`./..#", "#`...`..``.`./#/....#`#`/`/`...`.#``.#....//.``/.#", "../#../.`./`.```/..`..`..`/`/`.`././.`#`.`/....`.#", "#.../#/../..../...#/.//....`/.`...`..../`.#///...#", "#/.../`/`//.`.`/`...`/..#`#...`/..../.`./..`/#.`/#", "#`//`.#``/...///..`.`/#/#..#../.`.`.`./#./`/./..`#", "#...``././//`.```/...``...``.#/`....#../...``./#.#", "##./#/.../../`````#./.#..`/.///././/`..`#/..`#`###", "#.``.`///.`...`/.``...#....#../..`#/`.`/.`.......#", "###..#.`/....../#.#`/./...#.`....././.`#/..`..//.#", "#.`/#.#/`..//#``././..`/#/.`.`...`#./.`../.`/..#.#", "#/.//.#./..``./`../.`#/`/`.``/..`/..../`/`.`.....#", "#..`.///``//.../``#/.``.#...#`/.#..././..#`.#./#.#", "#/..../#...#``../././.```.`.#.#..`#/#.`.`..`/`#./#", "#``./.#/.//``..#`../#`.`.....#/./..##./..``.//...#", "#`#`/.`/`/.#/#`/`...#/.#//.`.../``//.//`#...../..#", "#/././/.//`.../.``..#/`.#`/`//../../..../..`..`//#", "#..`.```.....``../.`./#./`....././............`.##", "##.///`#`..`/`/.#`/..``#.#`....`````..../.```....#", "#/.#``....`.`#/...`#..#`.``..#`.....`.`.``/.##.`.#", "#..#``#/./.....//./``...#.`....//.../......#../..#", "#..#.//`///..#/...#/.`.`//..../#//....../``./``./#", "#./......#./#..`..//`.```/`#//.`./././/.##...`../#", "#.`#...../.#.`./......``#`/...`/``#./././..//.`./#", "##``.....`#....#/..`.../#.#`##/..#.`..../..//.``.#", "#.`/`/....`#..`./..`./#`#/`../`.........#/#......#", "##`.././..//`/./`.#....././...../`/.../...././..`#", "#....`.```..#`..`...//.`./..`#`..``..`/.....###`.#", "#././....../../`..`.##...####//./`.`..`.`#//`.```#", "#.......//.``/.`.``../.`.../.`#/../..`/...../.`./#", "#`/.....`.#`//.`/..#``//`..#`#..`.`./#``.#`.#.#/.#", "#.`.//#`#/.`....../.#.`././#/../`/....#/#/`.``/..#", "#/```..`.`.`.#.`/./../`.#..`////./..#..`...`#/...#", "#./..`.`..#``..`..`///.//...`...`..```../#`..`.``#", "#`......`./``.....`#```./#/.../#./../.``.#.`/..`.#", "#`.`#.#....../.`/#..//./`.`./`./.`###./././...`...", "##../.../`...``...`.`.`./#./`#.../#`.#`.```/#.#/.#", "#/./`.....`.```#..`../.`.```/.###//`./``....`#/#.#", "#`..#.`.../../`#.//..##..##/..././..`##`.`/#.`#.##", "#``/`.`.#...../...../.../.``##/...`./``./##.#//`.#", "#.##`///...../.`.##/.`/...`./.../``/.//./`./..`.##", "##################################################" }

    Returns: 21

24. { "################################.#################", "#/.`.#/`.`.`//#.`../..../.``.`......`..##/.......#", "#`...``/#`#././...``/./././`.#./../`.`#...##/##./#", "##......`#.##..`.#././...`../`/`/..`.`./...`#//..#", "#`.`..#.....`../##./.`./`#``/....#./#.`/##.``/#..#", "#../..#/..`.//..//...`.`...`......``.`./.#./..``/#", "#`../......./...///`.`../...`.`#./....`/`/./....`#", "#.../`#`././//.``./..../.`/...`/``./#/``#//......#", "#/.`.../.#/...`../``..//`..//../..`/.``.#.`/..#``#", "#/`...#./..`.............`.`././`./../.##../.#.`.#", "#/..../..`../..``../#`..``../././...``.//..../`..#", "#/.../``./`.`/.//...../.`.../#``/.``/`#.#//.`#//##", "#.`....`.../`..#.`//.`/.#/`.#`.`....../...`//....#", "#.#.``//`..`../.`../../`..././/..#/`../..#../#`.##", "#./`/./#.`#//`././....`/#.#.`./`....`.`#//#//`.//#", "#...#/./.../`#.#/..../##.`...`/./`...#`..//.`/...#", "#.`/``././`./.../.``./...#....`.``.``/`.../.`.`###", "#.//........./`..`.`.`/``.`..#..#/`./.`##/..`#..##", "##......`/`#``/.`.....//`...#`.#././...``./.`....#", "#..#.``/`.#..`//`/#.`../.#/.#.././/`#./../`/`....#", "#/#`.../#``#.`#`..`/#./`....././.`..`../../../.`.#", "#//`../..`.`.`......`.`//.`/.`./`./#..`#./.#...//#", "#./#.#///.`..``.....`/.#./#/#....././..`./`#../.##", "#`..#//#./.`.`....`....``...``#`./../`...#///`../#", "#/..`...`./.``#.../.```..`.#./.../.`##```./```../#", "#`..`..`.#/.....##...#`..`.`./```.#/#/...`##.``./#", "#..``##//`#.`#.../..`.#//#//#`...//.#../...`./#..#", "#/.`../.#..//...//```.../``.#./././...#../.../...#", "#`../..///.`/./``.#/..`....`..`/`#.//.``.#.#/...##", "#`.`/././/``.#`#..`/./#.`#..`../../.....#..`.././#", "#.`#..`.`/#//.....`/.#/.`.././/##.`/.......#..../#", "#.../././.`....`.`/.##..../..`.`/......./.../..`/#", "#./`.`.#...#/#....`/`.`../.`./#...`...#.././`.`.`#", "#..`/`../`/.#./`..`....././#/.`#/./.``../...../###", "#`..#....`./...../.......`//#/./...../..`//..`..`#", "#`/.../....//.../`/#/#`##`..`/`./`...#.```...//#.#", "#.`.`./.../`......./#`#`..`...`/...`.#/.../.#.#..#", "#.//....`..``.``....#`#/.#..`./#/.#``.....`..//`/#", "#..#`...#.``../#.#..`....//..#.``./``.....#.`.//.#", "###`./.#..///``#.``./././/`.`.`.`#/..#././...#/./#", "#``#/....././#/..`#``/`.///..#.../`./``..`/`.....#", "#...`/.``./`..`#.`/`./#.#..`.`./..``./`##.`./#..`#", "#..../`./#..#../..`..#`/`...`/.`//#...`/#`...../##", "#/`..#..#`/``.##./.##.//``#//.`/./``../../`#/.``.#", "#./...`//.`.#././../....././...``.`.`.`..``./....#", "##`.``../#`.`/../.`.../..`...##.//.##..#.///././.#", "#./```/`.`.....`.#.``.``.`/`...//....../..../..`##", "#`....`../.#..#`..``..`../.......#.....#..``#/`//#", "#./.`##`../.`..//../.../`/``/``/.../..``.#../...`#", "#################################.################" }

    Returns: 13

25. { "##################################################", "#///#///.`.`/.`#`##.#..#.`././/#//`..#../../`/#./#", "#/./`../.#.``/....../#./.#`.`....`..//`....`/./#.#", "##`./``/...``...#/#..`.`.#./#./././//`.#..`.//#`.#", "#//`..``.#../`...```./.#/....`#`../...``#`..``..`#", "##``..`/``././/./..#///.``../...//#`./././..#./`.#", "#/.#..#.#....``.`./...//....``/..`.#`..`.``/./../#", "##..``/.`/`/.`.`...##/...../..```...`...././.`../#", "#./.``/...../..#`..`.`#..../`.`/##.#`./.``..#`#/##", "#/`.`..//.#.../..#//.`.`..../`/#..../#/.../`././.#", "#.`.....#./`...```.`./.......`.`.``../`/..`.../..#", "#..`/.`./././.`/#../.`../.../`/.`..``..`..`/..`..#", "#/`...//`.`//...././##``///.//`../.`....`../.././#", "#```#`/....`....``../`.```........`//.```../`.`/##", "#.../#/`#/`#.###/.///#/./`//..#//...`///.`.`/....#", "#/#..`.`../#...`/./...`.#...#../#/#.``..//#.#`.`.#", "#``#/#/.../.#..#./.`./...../#....`.#`/....`#`.``/#", "##...../`...//./#`.#//../......#/`..#```..`/`//..#", "#`.`/.//.`../#```/.`/...//.`.`#.`.`#...#..#.`/#.`#", "##.`#/.`#...```.#``.`../#..`#`.`...``./.`././.....", "#..``../.#.``./`.//`/./...#./.#.`.../.`./#.#././/#", "#./.#..`#...//./#./#/.`./```..../../#/`///...#`..#", "#.//.../#//````/.`.`./..##./`..```.``....``..`.#/#", "#/....../`/#.//./.`````//.../`.#.`.`/.`.``....../#", "#..#./`..`..`.`...#.`..#..#.#/./``..`.......##/``#", "#/.`.#``#`//`/`/`//..`/`../.......#`....`#./.`///#", "#..`/..`..`././.././/`#`./```/.`/..///../``./../##", "##/#.``../.....`.`/../../.../../..`../`/.``...#`.#", "#/``./#././/...////.`.......///.#/.`./`#/........#", "#/../..////`.#.#``..#/#/.`#/``#././.`##..``..`#./#", "#/#.`...##/../....`..`././`/.`..//./..../.#//#.###", "#/.....`./``/`#`#`.`.`.`...`#.#`....`.`.``/.///..#", "#....//``//./#...`....../`./...`.//......#/#/#..##", "#.#`/.#////`..../.../``...`#/.#./.`../../..`/....#", "#/.`./..`..`.//./.....`.`/`.`/`.`...`....#././/..#", "###.#.././..//``.../..`#/.`//.//.#/`.....`../#`..#", "#`/./.`.`#`../`/.`..``//..`..`../....`.`/#.`/...`#", "#..#./..`.`.../#//..../#./........../.#/`../..#`.#", "#/....`/#.#..../..`.``...`.`/#./``..../``././.#.`#", "#..``.``.../.../`#`..//`./#`../...../#...`/``..#.#", "#`.#`#....`.`//...`.`./`.`..#.#.`#./.##...`/./#./#", "#.//#.#.//./../..#../.`.`.../#/...//./.``.`./....#", "#/#./../```///...`.#`....././/.`/.`/`##....#.../##", "#`./`/#/..../.#..```...`../``.//.#/```...`./..`./#", "#...#/`/`/`.``..`#`.`/`````.//..//./..#.#..../...#", "#...`/#./.#```./`..`....``#`/.....`/./.`././/.`.##", "#`././/..`/..////./.....`#../`.#....`/.`#.`//``..#", "##`../.#../``...#../..`#.`./`..#````/#.#.##..`/./#", "##`/.`../....`./.#/`.//./.#/..`..`./..``#`...`...#", "#######.##########################################" }

    Returns: 9

26. { "################.#################################", "#`/`/`.././../.`..//`/..`/.../#...`...`...``/..`.#", "#....././/...`......`.`#``.../..`......#.#../.`./#", "#//`../..#...#`.`...`/...///`#.......`.`..`..`/..#", "##`../.`./...//.``.`.//`.``/#.`...``/........./#/#", "#....`/../../...#/.#.`#../...`#../``/...///.```/##", "#..//./`//.`./..`...#./`../#..``....#..`###.../#`#", "#.../....`##...#/./....`//`./`.`./```#.``#.`.`//`#", "#..#/`/./`.../`/..#.../.#`/./././#.`#.#.....#...`#", "##../.`///#..`#`//./#//./..#....#//#.`.``../`.../#", "##`#/```//`/.``#..../.`.`...///#`../.#.`..##....`#", "#`/..#`...`..#`../.#.#`./#......`.`../..``..../..#", "#`/......`../`#...##/#`#.../.`/./.....`//`/.//#``#", "#/..#///...../.../.`././.`/./.#//....`....///`..##", "#./../.`/````.`.../....`/.```/`./`/#.#.//`...///.#", "#.`.......`../`.`#./../.`#.`./.`#.//....###..##/.#", "#/././.../..#..../.`../..`#.`.#.#..``/`//...``...#", "#./`/`/`..###..#..##.../`#..//.#`/.../`..##.//...#", "#`.#.......`...../``......../`.``#/#``..#/..`/...#", "#/`/#....`/..../...../....//.`.//`..`/#../.`.``.`#", "#././....#`.`./../.`../``././.#............./.#..#", "#..`.`/``..`#./...#./`#`./.....`/`//...`..``/`...#", "#.#/../..../``#...##`..`.`/.`..//././......`.`..`#", "##/.`.../.`///.##..#/././`/..```....`..`./#`.///##", "#..#/./`./#./``.../..`.``.../../`..`/.//...`#../.#", "#/..#./...`......//`#..`.`#`....`....//.#/`.``/.`#", "#.....#.`../`//.....`/`.#..#.```.../.`...#/#/``./#", "#.`#/#`...`..`.#.`./`..../../..#...//#...#`.`.//`#", "#.`#...`....``.//`/#`.`/....`...`./#`...////`/.#.#", "#.`//..`..////./.````#`.`././/...`..././..#.``#`.#", "##`...#/`#./.`.../../##.`././.`/.../../#/../`...##", "#./......./.`./..//`...`.```.#.`/..`.......`./`#.#", "#./`.../.#..`.///.../##.//`./.`...#..//`.....#...#", "#....#..``#..../../.`....#././`..`...../.#`.....`#", "#./#//.##/......./..`/.#.`...#..//`...././`......#", "#..../.``/.##..#...`.///`/.#.......#/./#...#``#./#", "#`./.``..#..`/../.`././/./#```.//....##/`./.`/.//#", "#/`..#.`/`//.#///...#./`..//...../#..../#`/./../`#", "#`./`#.#`..#....//..//...#.....`...`./..`#`//../.#", "#./`##.#.`/#/#..//...`/#```/...`/``./././.```#//`#", "#..`..`....`..#`...#`./``...`/..`.#.`/.`/////#`./#", "#./``//../..`/##.//./../.#`..`./`..//`.`#.`/`..#.#", "#.`/../##.`/#./#../.`..`.#....//..`.###......./.##", "#...../`../...//`.././.`/..`./....#.`....`#.//`.`#", "#.##/.`.....##../...`..`/....`.....`/.``../....`.#", "#..`/`.//`.#/..../..``.....//.`.`..//./...#./`..`#", "#..`./`/#/.//../#..../`.#/../...../`./`/./.#``.``#", "##.``..#/.`/..../`.#/.`..``#`.//..#./.`/.`/..#./.#", "#.././``..//..`./`...`.././..#``.#..../.#/./...`.#", "###################################.##############" }

    Returns: 16

27. { "############################################.#####", "#`.`.....`.```##`.`###.``./#`#.//`..#/..`./...`.##", "#`.#..`.##/..```..././..``....##./`.#/``##..#.`..#", "#`..`#`....`#`/`#...//#/.#.#..#.`./..../...##.//`#", "#`.//``/..`.```#/`..``/`./#./`./.`##/#`/.`##`.//.#", "#`./`../..#``##./../#/###../#//.`/.#.#`/..../#../#", "##/./``#..##`/``.#./`##.#`#`#.`..#.`../#/`#.#/#.##", "#`.``..##./`.`.`../#.../.`././```#.#`#``/../.#...#", "#...`/``.......`//`##.`..`.///.`.`../#/.`...///.##", "#/#.`/.`..#/`...`#.#.`##./`.##`../#`.`#/#``.`##`##", "##.//.``/``##`#.#./.#/#`./`.`./....`.`#.../`##`./#", "#...#/#.``./....././...#`.#....#`.../#.`/##`#``#.#", "##..../.#.`.../#...`/../#``....#/##`./..../..#/`##", "#./##`/...#.`.`#`///#/./``#`/.###.##.###/.//.#..##", "#....``./...//.#...#.//`##/#/.#/`//.`##/..#/#./``#", "##.....#```##/#...././/#`/../#.//#`/#####`//.`#`/#", "#`...``//.``..//#..#``....`.#````/``##..../`.../##", "#.`.``#```...#.`.`./././`//##.././#./`./#...#/.#.#", "##.`//./..#./``.....`.#./#`#/``#..`.`.##../`..`.##", "#.`./###../##`#.`.`...///##./#./`#..##`.#...#.#..#", "##./.`.````###../..#./.`#../#.`.``../`../#./.#/./#", "#.#.#/`#.//.#.#./`.##/`/`#//.#.#..#.##.#`.//`##/`#", "##`#.``#./..//.##`.``#.`//#/..#.``.#/`..``..`//#`#", "#.`/#`..#`##/./`...#````..`/#`..#``#`/##/##.#..`.#", "##.#`.#`.`.../.../#.###/#.`.#.`###./`.#.....###..#", "#/#.../...#..`#.##/.`.//./.`##.#.`..``..#.`.#../.#", "#./`....../`#.``.``..//.#/`.#`..```/`/#..####....#", "#.#/.//..//`/./`.`##``#`##.`..``.`.....`././`/.`/#", "#.##`#/#../.##`.#`#/..`.`/...`#././`.....#`#./#//#", "#...#/.`...#`.`/#..//...`###``/`#.#./......#`./`.#", "#/./...#.`./...`.#``#/`..#/#..//`#..//.#..../#``.#", "#.#`#`.//#``..#`/./..`./#.```./..#.#`/`/#/#//`...#", "#..`.`.`#....`////`/#..`./`../##././`/..../..`//.#", "#`/...`.#`#.#.....##/``##`#.`#//`....`.#``#`#.####", "##`...#.../#.##`..#.``././``#..`#`##.//`...`./#/##", "#/..#`.#.`..##.`.##`.#..//`##..`//.#./`/#..#/`..##", "#.`.#.`.`.#/`/.../...`.#``....`.`...`/#/.`./`.##/#", "#....#``/``#`/.#`...`.`/.`##.#`.#///`//...``///./#", "#.#/./#`#`./.##/#/##/#..`..//#`/..`.....//#`###//#", "#.`#./#.`##./```/..#/#./.`../#`./`#...`/`#.##./#/#", "#../.``...`..###.#./#/#.`#..#./#/./.#./..../....##", "#/#/##..`/./.#.###/./`/`./`/#.#.#./.#.#`./`.`/``..", "#..###//#..#..../#..`.`.`.```#`..`#./.``#./`.#//`#", "##/.//.//...//#/`...`#..#`..#./.##/`##/.``.#..`#.#", "#`..#`#/..#``.#```#/...#`#`./`/```#..#`/.`.`#//.##", "#.#..#.##.#.../..#/.#`##.#...`/##/.`..#``#`..#``.#", "#....#`#...#/`.``../`.##/#`....#/`.``#../..`.....#", "#.../`/.``..`/`#./..``.`#.#/`/`./..`./``#`./#..//#", "#./.#/#./#..#/./.`##.#/#./#.#/....#//./``.#./#/``#", "##################################################" }

    Returns: -1

28. { "##################################################", "#./`../`../`../`../`../`../`../`../`../`../`../`.#", "#/..`/..`/..`/..`/..`/..`/..`/..`/..`/..`/..`/./.#", "#`.............................................`.#", "#.`.............................................`#", "#./............................................./#", "#/............................................./.#", "#`.............................................`.#", "#.`.............................................`#", "#./............................................./#", "#/............................................./.#", "#`.............................................`.#", "#.`.............................................`#", "#./............................................./#", "#/............................................./.#", "#`.............................................`.#", "#.`.............................................`#", "#./............................................./#", "#/............................................./.#", "#`.............................................`.#", "#.`.............................................`#", "#./............................................./#", "#/............................................./.#", "#`.............................................`.#", "#.`.............................................`#", "#./............................................./#", "#/............................................./.#", "#`.............................................`.#", "#.`.............................................`#", "#./............................................./#", "#/............................................./.#", "#`.............................................`.#", "#.`.............................................`#", "#./............................................./#", "#/............................................./.#", "#`.............................................`.#", "#.`.............................................`#", "#./............................................./#", "#/............................................./.#", "#`.............................................`.#", "#.`.............................................`#", "#./............................................./#", "#/............................................./.#", "#`.............................................`.#", "#.`.............................................`#", "................................................/#", ".............................................../.#", "#./.../`../`../`../`../`../`../`../`../`../`...`.#", "#.`/`/..`/..`/..`/..`/..`/..`/..`/..`/..`/..`/`/.#", "##################################################" }

    Returns: 0