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;
typedef long long ll;
#define rep(i, N) for (int i = 0; i < (int)N; i++)

const int INF = 1e9;
const int MAX_V = 100;

struct edge { int to, cap, rev; };

vector<edge> G[MAX_V];
bool used[MAX_V];

void addEdge(int from, int to, int cap){
  G[from].push_back((edge) {to, cap, static_cast<int>(G[to].size())});
  G[to].push_back((edge) {from, 0, static_cast<int>(G[from].size()) - 1});
}

int dfs(int v, int t, int f) {
  if(v == t) return f;
  used[v] = true;
  for(int i = 0; i < G[v].size(); i++){
    edge &e = G[v][i];
    if(!used[e.to] && e.cap > 0) {
      int d = dfs(e.to, t, min(f, e.cap));
      if (d > 0) {
        e.cap -= d;
        G[e.to][e.rev].cap += d;
        return d;
      }
    }
  }
  return 0;
}

int maxFlow(int s, int t) {
  int flow = 0;
  while(true) {
    memset(used, 0, sizeof(used));
    int f = dfs(s, t, INF);
    if( f == 0 ) return flow;
    flow += f;
  }
}


int main () {
  int V, E;
  cin >> V >> E;

  for(int i = 0; i < E; i++){
    int u, v, c;
    cin >> u >> v >> c;
    addEdge(u, v, c);
  }

  cout << maxFlow(0, V-1) << endl;
  return 0;
}

