**Time limit:**1.00 s**Memory limit:**512 MB

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.