Problem Description

This is a template problem.

Given $n$ vertices and $m$ directed edges, each with a specified capacity, determine the maximum flow from vertex $s$ to vertex $t$.

Input Format

The first line contains four integers $n$, $m$, $s$, and $t$.
The following $m$ lines each contain three integers $u$, $v$, and $c$, representing a directed edge from vertex $u$ to vertex $v$ with a capacity $c$.

Output Format

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

Example 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

Example Output

14

Constraints and Hints

• $1 \leqslant n \leqslant 100$
• $1 \leqslant m \leqslant 5000$
• $0 \leqslant c \leqslant 2^{31} - 1$