CSES - HIIT Open 2019 - HIIT Speedrun
• Time limit: 1.00 s
• Memory limit: 512 MB
You are playing a game that consists of $n$ rooms and $m$ tunnels between them. Each room has a letter that you can collect.

Your task is to move from room $1$ to room $n$ and collect one letter H, two letters I and one letter T during your journey. You can collect the letters in any order. What is the minimum length of such a path?

Input

The first input line has two integers $n$ and $m$: the number of rooms and tunnels. The rooms are numbered $1,2,\dots,n$.

The second line has $n$ characters $c_1 c_2 \dots c_n$: the letter (A–Z) in each room.

Finally, there are $m$ lines that describe the tunnels. Each line has two integers $a$ and $b$: there is a tunnel between rooms $a$ and $b$.

Output

Print one integer: the minimum length of a valid path from room $1$ to room $n$. If there is no such path, print "IMPOSSIBLE".

Constraints
• $1 \le n \le 100$
• $0 \le m \le 5000$
Example 1

Input:
5 6 ITHXI 1 2 1 3 1 4 3 4 3 5 4 5

Output:
4

Explanation: An optimal path is $1 \rightarrow 2 \rightarrow 1 \rightarrow 3 \rightarrow 5$.

Example 2

Input:
3 2 HIT 1 2 2 3

Output:
IMPOSSIBLE

Explanation: Only one letter I is available, so you can't win the game.