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;
using UL=unsigned int;
using LL=long long;
using ULL=unsigned long long;
#define rep(i,n) for(UL i=0; i<(n); i++)

struct Edge{ UL u,v; UL c; UL r; };

UL N,M;
vector<UL> E[100];
Edge J[2000];

UL fD[100];
UL fF[100];
UL fAns;

UL fDFS(UL p,UL c=10000000){
 if(p==N-1) return c;
 UL f=0;
 for(UL& i=fF[p]; i<E[p].size(); i++){
  Edge& e = J[E[p][i]];
  if(c-f==0) return f;
  if(fF[e.v]) continue;
  if(e.c==0) continue;
  if(fD[e.v]!=fD[p]+1) continue;
  UL tmp = fDFS(e.v,min(c-f,e.c));
  e.c -= tmp; J[e.r].c += tmp;
  f += tmp;
 }
 return f;
}

UL flow(){
 rep(i,N) fD[i]=~0u;
 fD[0]=0;
 queue<UL> Q; Q.push(0);
 while(Q.size()){
  UL p=Q.front(); Q.pop();
  for(UL j:E[p]){
   if(fD[J[j].v]!=~0u) continue;
   if(J[j].c==0) continue;
   fD[J[j].v]=fD[p]+1;
   Q.push(J[j].v);
  }
 }
 rep(i,N) fF[i]=0;
 UL res=fDFS(0);
 fAns += res;
 return res;
}

int main(){
 scanf("%u%u",&N,&M);
 rep(i,M){
  UL u,v,c; scanf("%u%u%u",&u,&v,&c);
  J[i]={u,v,c,M+i};
  J[M+i]={v,u,0,i};
  E[u].push_back(i);
  E[v].push_back(M+i);
 }
 while(flow());
 printf("%u\n",fAns);
 return 0;
}

