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문제

A bracket symbol is one of the following: ()[]\{\}<>. A correct \textit{bracket expression} is any string consisting of bracket symbols, such that:

  • Every left bracket has a matching right bracket of the same kind, and every right bracket is matched;
  • No two pairs of matching brackets cross -- for every two such pairs, they are either disjoint or one is contained inside the other.

For example, ([])<> is a correct bracket expression, whereas <{>} is not, as the curly brackets and angle brackets cross each other.

You are given a graph of $n$ vertices in which every (directed) edge is labeled with one of the bracket symbols. A path in this graph is valid, if its edges form a correct bracket expression. For some two vertices $s$ and $t$, determine the length of a shortest valid path between $s$ and $t$. We allow the path to pass multiple times through any vertex.

입력

On the first line of input there are four integers $n, m, s, t$ ($1 \leq n \leq 200$, $0 \leq m \leq 2000$, $1 \leq s, t \leq n$) -- the number of vertices, edges, starting and ending vertex, respectively.

Each of the following $m$ lines contains two integers $x$, $y$ and a bracket symbol $b$ ($1 \leq x, y \leq n$), which describe one graph edge. Note that there may be loops and multiple edges.

출력

Output a single line containing a single integer -- the length of the shortest valid path between $s$ and $t$. If there is no such path, output $-1$. You may assume that if a path exists, its length does not exceed $10^{18}$.

예제 입력 1

4 4 1 4
1 2 (
2 2 [
2 3 ]
3 4 )

예제 출력 1

4

예제 입력 2

5 4 1 5
1 2 <
2 3 {
3 4 >
4 5 }

예제 출력 2

-1