## Maze Pathfinder |

This problem is very simple: just find the way out of the maze.

*Hint: you can choose any algorithm you know/like but a kind of wave propagation method is recommended.*

Maze is given as a rectangular matrix of `0`

and `1`

characters. Exit is in `top-left`

corner. You are to find the ways
from `top-right`

, `bottom-left`

and `bottom-right`

corners, i.e.

```
X-----A 1110001
------- 0010001
------- 1111111
------- 0000101
B-----C 1111101
```

For example in `7 * 5`

rectangle (on the left) we should find ways from corners `A`

, `B`

and `C`

to corner `X`

.
And for topology given (on the right) paths should be:

```
from A: DDLLLLUULL
from B: RRRRUULLUULL
from C: UULLLLUULL
```

Where `U`

denotes step up, `L`

is one step left, `R`

and `D`

are steps right and down respectively. We will use short
form like:

```
from A: 2D4L2U2L
from B: 4R2U2L2U2L
from C: 2U4L2U2L
```

You see, each letter is preceded by amount of steps in this direction, like - 2 down, 4 left, 2 up, 2 left etc.

**Input data** will contain width and height of the maze in first line (both are odd values).

Then maze itself will follow, with `1`

depicting passages and `0`

for impassable walls.

**Answer** should contain three paths, space separated, in the format explained above.

Example:

```
input data:
13 9
1111101110111
0010001000001
1011111111111
1000000010100
1111111110101
0010000010001
1111101010111
1010001000100
1011111111111
answer:
2D10L2U2L 2U2R2U6R2U6L2U2L 10L4U6R2U6L2U2L
```

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