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 flow{
	int n,s,t;
	struct edge{
		int from,to,cap;
		edge(int f,int t,int c):from(f),to(t),cap(c){}
	};
	vector<edge>e;
	vector<vector<int> >v;
	flow(int n,int s,int t):n(n),s(s),t(t),v(n){}
	
	
	void addedge(int s,int t,int c){
		v[s].emplace_back(e.size());
		e.emplace_back(s,t,c);
		v[t].emplace_back(e.size());
		e.emplace_back(t,s,0);
	}
	vector<int>dist,par;
	int minedge;
	int bfs(){
		for(int i=0;i<n;i++){
			par[i]=-1;
			dist[i]=INT_MAX;
		}
		
		dist[s]=0;
		queue<int>q;
		q.emplace(s);
		while(!q.empty()){
			int u=q.front();
			q.pop();
			for(int i=0;i<v[u].size();i++){
				if(e[v[u][i]].cap<=0){
					continue;
				}
				if(dist[e[v[u][i]].to]==INT_MAX){
					dist[e[v[u][i]].to]=dist[u]+1;
					par[e[v[u][i]].to]=v[u][i];
					q.emplace(e[v[u][i]].to);
				}
			}
		}
		return dist[t];
	}
	int aug(){
		minedge=INT_MAX;
		for(int i=t;par[i]!=-1;i=e[par[i]].from){
			minedge=min(e[par[i]].cap,minedge);
		}
		for(int i=t;par[i]!=-1;i=e[par[i]].from){
			e[par[i]].cap-=minedge;
			e[par[i]^1].cap+=minedge;
		}
		return minedge;
	}
	int maxflow(){
		int flowrate=0;
		for(int i=0;i<n;i++){
			par.emplace_back(-1);
			dist.emplace_back(INT_MAX);
		}
		while(bfs()!=INT_MAX){
			
			flowrate+=aug();
		}
		return flowrate;
	}
};
int main(){
	int n,m;
	cin>>n>>m;
	flow f(n,0,n-1);
	while(m--){
		int s,t,c;
		cin>>s>>t>>c;
		f.addedge(s,t,c);
	}
	
	cout<<f.maxflow()<<"\n";
}
