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
#pragma GCC optimize("Ofast", "unroll-loops")

#include <bits/stdc++.h>

using namespace std;

#define ll long long

template<typename T>
struct Graph {
	struct edge {
		int to, rev;
		T cap;
		edge(int to, int rev, T cap) : to(to), rev(rev), cap(cap) {}
	};

	int n;
	vector<vector<edge>> g;
	vector<bool> used;

	Graph(int n) : n(n), g(n) {}

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

	T dfs(int v, int t, T f) {
		if (v == t) return f;
		used[v] = true;
		for (int i = 0; i < g[v].size(); ++i) {
			edge& e = g[v][i];
			if (!used[e.to] && e.cap > 0) {
				T 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 (T)0;
	}

	T max_flow(int s, int t) {
		T res = 0;
		while (1) {
			used = vector<bool>(n, false);
			T tmp = dfs(s, t, numeric_limits<T>::max());
			if (tmp == 0) break;
			res += tmp;
		}
		return res;
	}
};

int main(void) {
	int V, E;
	cin >> V >> E;
	Graph<ll> g(V);
	while (E--) {
		int u, v; ll c;
		cin >> u >> v >> c;
		g.add_edge(u, v, c);
	}
	cout << g.max_flow(0, V - 1) << endl;
	return 0;
}
