A flow network is a directed graph which has a $source$ and a $sink$. In a flow network, each edge $(u, v)$ has a capacity $c(u, v)$. Each edge receives a flow, but the amount of flow on the edge can not exceed the corresponding capacity. Find the maximum flow from the $source$ to the $sink$.

Constraints

* $2 \leq |V| \leq 100$
* $1 \leq |E| \leq 1000$
* $0 \leq c_i \leq 10000$

Input

A flow network is given in the following format.

$|V|\;|E|$
$u_0\;v_0\;c_0$
$u_1\;v_1\;c_1$
:
$u_{|E|-1}\;v_{|E|-1}\;c_{|E|-1}$



$|V|$, $|E|$ is the number of vertices and edges of the flow network respectively. The vertices in $G$ are named with the numbers 0, 1,..., $|V|-1$. The source is 0 and the sink is $|V|-1$.

$u_i$, $v_i$, $c_i$ represent $i$-th edge of the flow network. A pair of $u_i$ and $v_i$ denotes that there is an edge from $u_i$ to $v_i$ and $c_i$ is the capacity of $i$-th edge.

Output

Print the maximum flow.

Example

Input

4 5
0 1 2
0 2 1
1 2 1
1 3 1
2 3 2


Output

3
#include "bits/stdc++.h"
using namespace std;

struct edge { int to, cap, rev; };

vector<edge> G[110];
int level[110];
int iter[110];
int INF = 1000000000;

void add_edge(int from, int to, int cap) {
	G[from].push_back({ to, cap, (int)G[to].size() });
	G[to].push_back({ from, 0, (int)G[from].size() - 1 });
}

void BFS(int S) {
	memset(level, -1, sizeof(level));
	queue<int> Q;
	level[S] = 0;
	Q.push(S);
	while (!Q.empty()) {
		int V = Q.front(); Q.pop();
		for (int i = 0; i < G[V].size(); i++) {
			edge& E = G[V][i];
			if (E.cap > 0 && level[E.to] < 0) {
				level[E.to] = level[V] + 1;
				Q.push(E.to);
			}
		}
	}
}

int DFS(int V, int T, int F) {
	if (V == T) return F;
	for (int &i = iter[V]; i < G[V].size(); i++) {
		edge& E = G[V][i];
		if (E.cap > 0 && level[V] < level[E.to]) {
			int D = DFS(E.to, T, min(F, E.cap));
			if (D > 0) {
				E.cap -= D;
				G[E.to][E.rev].cap += D;
				return D;
			}
		}
	}
	return 0;
}

int max_flow(int S, int T) {
	int flow = 0;
	for (;;) {
		BFS(S);
		if (level[T] < 0) return flow;
		memset(iter, 0, sizeof(iter));
		int F;
		while ((F = DFS(S, T, INF)) > 0) {
			flow += F;
		}
	}
}

int main() {
	int V, E;
	cin >> V >> E;
	for (int i = 0; i < E; i++) {
		int v, e, c;
		cin >> v >> e >> c;
		add_edge(v, e, c);
	}
	cout << max_flow(0, V - 1) << endl;
}
