# Problem G

Escape Wall Maria

Wall Maria has been broken! Eren must evacuate as soon as possible from his house. He must find the fastest route to escape within Wall Maria before the titans rush in. Wall Maria is represented as a $N \times M$ grid in which Eren can move horizontally or vertically.

There are burning houses and buildings which prevent Eren
from passing through them. The burning houses and buildings are
represented as ‘`1`’. Unburned or safe
areas are represented as ‘`0`’. There
are some areas which can be entered but only from a specific
direction. These areas can be represented by either ‘`U`’, ‘`D`’, ‘`L`’, or ‘`R`’. For
example, if there is an ‘`R`’ that
means that area can only be entered from the right neighboring
tile within Wall Maria’s grid. Similarly, ‘`U`’ tiles can only be entered from above,
‘`D`’ tiles can only be entered from
below, and ‘`L`’ tiles can only be
entered from the left.

Eren knows the time $t$ at which the titans will rush in. It takes $1$ unit of time to traverse $1$ zone (which corresponds to $1$ tile in the grid). Once he reaches any border of Wall Maria he is safe.

Eren’s starting position is represented by the letter
‘`S`’. If Eren escapes at or before
time $t$, he is safe.
Given his position within Wall Maria determine if it is
possible to escape. If it is possible determine the number of
zones that must be traversed to lead to the quickest
escape.

## Input

The input consists of a single test case. The first line
contains three integers $t$ ($1
\le t \le 200$) , $N$ ($1
\le N \le 100$) and $M$ ($1
\le M \le 100$). The rest of N lines will be Wall
Maria’s grid containing characters ‘`1`‘, ‘`0`‘, ‘`S`‘, ‘`U`‘, ‘`D`‘, ‘`L`‘, or
‘`R`‘. There is exactly one ‘`S`‘ in the input.

## Output

If it is possible to escape Wall Maria, output the minimum
number of zones that must be traversed to escape. If it is not
possible to escape, print “`NOT
POSSIBLE`”!

Sample Input 1 | Sample Output 1 |
---|---|

2 4 4 1111 1S01 1011 0U11 |
2 |

Sample Input 2 | Sample Output 2 |
---|---|

2 4 4 1111 1S01 1011 0L11 |
NOT POSSIBLE |

Sample Input 3 | Sample Output 3 |
---|---|

1 4 4 1S01 1001 1011 0U11 |
0 |