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 <iostream>
#include <vector>
#include <algorithm>

#define rep(i,n) for(int i=0; i<(n); i++)

using namespace std;
typedef pair<int,int> pii;

const int INF = 0x3fffffff;

class Flow{
	public:
		int N, en;
		vector< vector<int> > F, C;
		vector< vector<pii> > edge;
		Flow(int n, int e): F(n,vector<int>(n)), C(n,vector<int>(n)), N(n), edge(n){ en=0; }
		void addEdge(int f, int t, int c){
			F[f][t] = C[f][t] = c;
		}
		int flow(int n, int c, int T, vector<bool> &bf){
			if( n == T ) return c;
			bf[n] = true;
			rep(i,N){
				if( F[n][i] > 0 && !bf[i] ){
					int f = flow(i, min(c, F[n][i]), T, bf);
					if( f > 0 ){
						F[n][i] -= f;
						F[i][n] += f;
						return f;
					}
				}
			}
			return 0;
		}
		int maxFlow(int S, int T){
			for(int ret=0;;){
				vector<bool> bf(N);
				int add = flow(0, INF, T, bf);
				ret += add;
				if( add==0 ) return ret;
			}
		}
		void clear(){
			//fill( F.begin(), F.end(), 0 );
		}
};

int main(){
	int V, E;
	cin >> V >> E;
	Flow fl(V,E);
	for(int i=1; i<=E; i++){
		int u, v, c;
		cin >> u >> v >> c;
		fl.addEdge( u, v, c );
	}

	cout << fl.maxFlow(0, V-1) << endl;

	return 0;
}