#include <iostream>
#include <climits>


const int inf = INT_MAX / 3;
const int max_v = 16;

int d[max_v][max_v];
int dp[(1 << max_v) - 1][max_v];  // S?????¢????????£????????????????????????v??????????????´???


using namespace std;

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

	for (int i = 0; i < V; i++) {
		for (int j = 0; j < V; j++) {
			d[i][j] = (i == j) ? 0 : inf;

		}
	}

	for (int i = 0; i < E; i++) {
		int ts,tt , td;
		cin >> ts >> tt >> td;
		d[ts][tt] = td;
	}

	for (int s = (1 << V) - 1; s >= 0; s--) {
		for (int v = 0; v < V; v++) {
			dp[s][v] = inf;
		}
	}

	dp[(1 << V) - 1][0] = 0;

	for (int s = (1 << V) - 1; s >= 0; s--) {
		for (int v = 0; v < V; v++) {
			for (int u = 0; u < V;u++) {
				//cout << "s:" << s << " v:" << v << " u:" << u << endl;
				if (!((s >> u) & 1)) {
					dp[s][v] = min(dp[s][v], dp[s | 1 << u][u] + d[u][v]);
				//	cout << " dp:" << dp[s][v] << endl;

				}
			}
		}
	}

	if (dp[0][0] >= inf) {
		cout << -1 << endl;
	} else {
		cout << dp[0][0] << endl;
	}
	return 0;
}
### Prompt

Develop a solution in Cpp to the problem described below:

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 <iostream>
#include <climits>


const int inf = INT_MAX / 3;
const int max_v = 16;

int d[max_v][max_v];
int dp[(1 << max_v) - 1][max_v];  // S?????¢????????£????????????????????????v??????????????´???


using namespace std;

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

	for (int i = 0; i < V; i++) {
		for (int j = 0; j < V; j++) {
			d[i][j] = (i == j) ? 0 : inf;

		}
	}

	for (int i = 0; i < E; i++) {
		int ts,tt , td;
		cin >> ts >> tt >> td;
		d[ts][tt] = td;
	}

	for (int s = (1 << V) - 1; s >= 0; s--) {
		for (int v = 0; v < V; v++) {
			dp[s][v] = inf;
		}
	}

	dp[(1 << V) - 1][0] = 0;

	for (int s = (1 << V) - 1; s >= 0; s--) {
		for (int v = 0; v < V; v++) {
			for (int u = 0; u < V;u++) {
				//cout << "s:" << s << " v:" << v << " u:" << u << endl;
				if (!((s >> u) & 1)) {
					dp[s][v] = min(dp[s][v], dp[s | 1 << u][u] + d[u][v]);
				//	cout << " dp:" << dp[s][v] << endl;

				}
			}
		}
	}

	if (dp[0][0] >= inf) {
		cout << -1 << endl;
	} else {
		cout << dp[0][0] << endl;
	}
	return 0;
}
```