#include <iostream>
#include <algorithm>
using namespace std;
#define INF 10000000
int V, E;
int dp[1 << 16][20] = { 0 }, d[20][20] = { 0 };
int main() {
	for (int i = 0; i < (1 << 16); i++) {
		for (int j = 0; j < 20; j++) {
			dp[i][j] = INF;
		}
	}
	for (int i = 0; i < 20; i++) {
		for (int j = 0; j < 20; j++) {
			d[i][j] = INF;
		}
	}
	cin >> V >> E;
	for (int i = 0; i < E; i++) {
		int s, t, c;
		cin >> s >> t >> c;
		d[s][t] = c;
	}
	dp[1][0] = 0;
	for (int i = 0; i < (1 << V); i++) {
		for (int j = 0; j < V; j++) {
			if ((i >> j) & 1) {
				for (int k = 0; k < V; k++) {
					if ((i >> k) & 1) continue;
					dp[i | (1 << k)][k] = min(dp[i | (1 << k)][k], dp[i][j] + d[j][k]);
				}
			}
		}
	}
	int res = INF;
	for (int i = 0; i < V; i++) {
		res = min(res, dp[(1 << V) - 1][i] + d[i][0]);
	}
	if (res == INF) res = -1;
	cout << res << endl;
	return 0;
}

### Prompt

Please formulate a Cpp solution to 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 <iostream>
#include <algorithm>
using namespace std;
#define INF 10000000
int V, E;
int dp[1 << 16][20] = { 0 }, d[20][20] = { 0 };
int main() {
	for (int i = 0; i < (1 << 16); i++) {
		for (int j = 0; j < 20; j++) {
			dp[i][j] = INF;
		}
	}
	for (int i = 0; i < 20; i++) {
		for (int j = 0; j < 20; j++) {
			d[i][j] = INF;
		}
	}
	cin >> V >> E;
	for (int i = 0; i < E; i++) {
		int s, t, c;
		cin >> s >> t >> c;
		d[s][t] = c;
	}
	dp[1][0] = 0;
	for (int i = 0; i < (1 << V); i++) {
		for (int j = 0; j < V; j++) {
			if ((i >> j) & 1) {
				for (int k = 0; k < V; k++) {
					if ((i >> k) & 1) continue;
					dp[i | (1 << k)][k] = min(dp[i | (1 << k)][k], dp[i][j] + d[j][k]);
				}
			}
		}
	}
	int res = INF;
	for (int i = 0; i < V; i++) {
		res = min(res, dp[(1 << V) - 1][i] + d[i][0]);
	}
	if (res == INF) res = -1;
	cout << res << endl;
	return 0;
}

```