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<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll n,m,a,b,c,flow,used[101];
struct edge{ll to,cap,rev;};
vector<edge>v[101];
ll dfs(ll s,ll t,ll f){
    if(s==t)return f;
    used[s]=1;
    for(int i=0;i<v[s].size();i++){
        edge &u=v[s][i];
        if(used[u.to]==0&&u.cap>0){
            ll d=dfs(u.to,t,min(f,u.cap));
            if(d>0){
                u.cap-=d;
                v[u.to][u.rev].cap+=d;
                return d;
            }
        }
    }
    return 0;
}
int main(void){
    cin>>n>>m;
    for(int i=0;i<m;i++){
        cin>>a>>b>>c;
        //edge ed1={b,c,v[b].size()};
        v[a].push_back({b,c,(ll)v[b].size()});
        v[b].push_back((edge){a,0,(ll)v[a].size()-1});//v[a].size()-1});
    }
    while(1){
        for(int i=0;i<101;i++)used[i]=0;
        ll f=dfs(0,n-1,1LL<<60);
        flow+=f;
        if(f==0){
            cout<<flow<<endl;
            return 0;
        }
    }
}

