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;

#define ll long long

ll N, M;
vector<vector<pair<ll, ll> > > G;

ll edo(ll zac, ll kon){
	ll F = 0;
	while(true){
		queue<ll> Q;
		vector<ll> vzd(N, -1), pred(N, -1), tok(N);
		Q.push(zac);
		vzd[zac] = 0;
		tok[zac] = LONG_LONG_MAX;
		while(Q.size() != 0){
			ll v = Q.front();
			Q.pop();
			for(ll w = 0; w < N; w++){
				ll f1 = G[v][w].first, f2 = G[w][v].first, c = G[v][w].second, r = c - f1 + f2;
				if(r > 0 && vzd[w] == -1){
					vzd[w] = vzd[v]++;
					pred[w] = v;
					tok[w] = min(tok[v], r);
					Q.push(w);
				}
			}
		}
		if(vzd[kon] == -1) break;
		F += tok[kon];
		ll v = kon;
		while(v != zac){
			ll w = pred[v], f1 = G[w][v].first, f2 = G[v][w].first, c = G[w][v].second, o = min(f2, tok[kon]);
			G[v][w].first -= o;
			G[w][v].first += tok[kon] - o;
			v = w;
		}
	}
	return F;
}


int main(){
	ios::sync_with_stdio(false);
	cin >> N >> M;
	G.resize(N, vector<pair<ll, ll> >(N, {0, 0}));
	for(ll m = 0; m < M; m++){
		ll A, B, C;
		cin >> A >> B >> C;
		G[A][B].second = C;
	}
	cout << edo(0, N-1) << endl;
	return 0;
}