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 int ll;
typedef vector<ll> vl;
typedef pair<ll, ll> PP;
#define rep(i,n) for(ll i = 0; i < ll(n); i++)
#define all(v) v.begin() , v.end()
#define inputv(v,n) rep(i,n){\
    ll x;\
    cin>>x;\
    v.push_back(x);\
    }
const ll INF = 999999999999999;
const ll MOD = 1000000007;
ll a, b, c, d, e, f, p, t, x, y, z, q, m, n, r, h, k, ans = 0, w, l;
struct edge { ll to, w, p; };
vector<edge>X[110];
int N, M, used[110];
ll dfs(ll s, ll t, ll r) {
	if (s == t)return r; used[s] = 1;
	for (int i = 0; i < ll(X[s].size()); i++) {
		edge& u = X[s][i];
		if (used[u.to] == 0 && u.w > 0) {
			ll F = dfs(u.to, t, min(r, u.w));
			if (F > 0) { u.w -= F; X[u.to][u.p].w += F; return F; }
		}
	}
	return 0;
}
void input() {
	cin >> N >> M;
	for (int i = 0; i < M; i++) {
		cin >> a >> b >> c;
		edge p = { b,c,ll(X[b].size()) }; X[a].push_back(p);
		edge q = { a,0,ll(X[a].size() - 1) }; X[b].push_back(q);
	}
	ll res = 0;
	while (true) {
		for (int i = 0; i < 110; i++)used[i] = 0;
		ll P = dfs(0, N - 1, 1 << 30);
		if (P == 0)break; res += P;
	}
	cout << res << endl;
}
void solve() {
	
}

int main() {
	input();
	solve();
}
