Maximum Flow

Problem Description

Given $n$ vertices, $m$ directed edges, and the capacity of each edge, find the maximum flow from vertex $s$ to vertex $t$.

Input Format

The first line contains four integers $n\ (1 \le n \le 100), m\ (1 \le m \le 5000), s, t$.

Each of the next $m$ lines contains three integers $u, v, c$, describing a directed edge from $u$ to $v$ with capacity $c\ (0 \le c \le 2^{31} - 1)$.

Output Format

Output the maximum flow from vertex $s$ to vertex $t$.

Sample Input

7 14 1 7
1 2 5
1 3 6
1 4 5
2 3 2
2 5 3
3 2 2
3 4 3
3 5 3
3 6 7
4 6 5
5 6 1
6 5 1
5 7 8
6 7 7

Sample Output

14