#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define INF 1<<30
#define LINF 1LL<<60

struct edge {
	ll u;
	ll v;
	ll cost;
	edge() {}
	edge(ll u, ll v, ll c) :u(u), v(v), cost(c) {}
};

int main(void) {
	cin.tie(0); ios::sync_with_stdio(false);
	ll V, E; cin >> V >> E;
	vector<vector<edge>> G(V);
	for (int i = 0; i < E;i++) {
		ll s, t, d; cin >> s >> t >> d;
		G[s].emplace_back(edge(s, t, d));
	}
	/* dp[i][j] := ?????????j???????????¨???, bit???i??????????????°????????§???????????????????????¢ */
	vector<vector<ll>> dp(1 << V, vector<ll>(V, INF));
	dp[0][0] = 0;
	for (int i = 0; i < (1 << V);i++) {
		for (int j = 0; j < V;j++) {
			for (auto e : G[j]) {
				if (!((i >> e.v) & 1)) {
					dp[i | (1 << e.v)][e.v] = min(dp[i | (1 << e.v)][e.v], dp[i][e.u] + e.cost);
				}
			}
		}
	}
	ll ret = dp[(1 << V) - 1][0];
	if (ret == INF)ret = -1;
	cout << ret << endl;
	return 0;
}
### Prompt

In CPP, your task is to solve the following problem:

For a given weighted directed graph G(V, E), find the distance of the shortest route that meets the following criteria:

* It is a closed cycle where it ends at the same point it starts.
* It visits each vertex exactly once.

Constraints

* 2 ≤ |V| ≤ 15
* 0 ≤ di ≤ 1,000
* There are no multiedge

Input


|V| |E|
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1


|V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively.

si and ti represent source and target vertices of i-th edge (directed) and di represents the distance between si and ti (the i-th edge).

Output

Print the shortest distance in a line. If there is no solution, print -1.

Examples

Input

4 6
0 1 2
1 2 3
1 3 9
2 0 1
2 3 6
3 2 4


Output

16


Input

3 3
0 1 1
1 2 1
0 2 1


Output

-1

### Response

```cpp
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define INF 1<<30
#define LINF 1LL<<60

struct edge {
	ll u;
	ll v;
	ll cost;
	edge() {}
	edge(ll u, ll v, ll c) :u(u), v(v), cost(c) {}
};

int main(void) {
	cin.tie(0); ios::sync_with_stdio(false);
	ll V, E; cin >> V >> E;
	vector<vector<edge>> G(V);
	for (int i = 0; i < E;i++) {
		ll s, t, d; cin >> s >> t >> d;
		G[s].emplace_back(edge(s, t, d));
	}
	/* dp[i][j] := ?????????j???????????¨???, bit???i??????????????°????????§???????????????????????¢ */
	vector<vector<ll>> dp(1 << V, vector<ll>(V, INF));
	dp[0][0] = 0;
	for (int i = 0; i < (1 << V);i++) {
		for (int j = 0; j < V;j++) {
			for (auto e : G[j]) {
				if (!((i >> e.v) & 1)) {
					dp[i | (1 << e.v)][e.v] = min(dp[i | (1 << e.v)][e.v], dp[i][e.u] + e.cost);
				}
			}
		}
	}
	ll ret = dp[(1 << V) - 1][0];
	if (ret == INF)ret = -1;
	cout << ret << endl;
	return 0;
}
```