#include<bits/stdc++.h>
using namespace std;

#define MAX_N 15
#define INF 100000

int n;
int t[MAX_N][MAX_N];

int dp[1 << MAX_N][MAX_N];

int rec(int s, int v) {
	if (dp[s][v] >= 0) {
		return dp[s][v];
	}

	if (s == (1 << n) - 1 && v == 0) return dp[s][v] = 0;

	int res = INF;
	for (int u = 0; u < n; u++) {
		if (t[v][u] != INF && !(s >> u & 1)) {
			res = min(res, rec(s | 1 << u, u) + t[v][u]);
		}
	}
	return dp[s][v] = res;
}

int main() {
	int m;

	cin >> n;
	cin >> m;

	for (int i = 0; i < (1 << n); i++) {
		for (int j = 0; j < n; j++) {
			dp[i][j] = -1;
		}
	}
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			t[i][j] = INF;
		}
	}

	for (int i = 0; i < m; i++) {
		int a, b, c;
		cin >> a >> b >> c;
		t[a][b] = c;
	}

	/*for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			cout << t[i][j] << " ";
		}
		cout << endl;
	}
	cout << endl;*/
	if (rec(0, 0) == INF) {
		cout << -1 << endl;
	}
	else {
		cout << rec(0, 0) << endl;
	}

	/*for (int i = 0; i < (1 << n); i++) {
		for (int j = 0; j < n; j++) {
			cout << dp[i][j] << " ";
		}
		cout << endl;
	}*/

	return 0;
}

### Prompt

Your task is to create 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<bits/stdc++.h>
using namespace std;

#define MAX_N 15
#define INF 100000

int n;
int t[MAX_N][MAX_N];

int dp[1 << MAX_N][MAX_N];

int rec(int s, int v) {
	if (dp[s][v] >= 0) {
		return dp[s][v];
	}

	if (s == (1 << n) - 1 && v == 0) return dp[s][v] = 0;

	int res = INF;
	for (int u = 0; u < n; u++) {
		if (t[v][u] != INF && !(s >> u & 1)) {
			res = min(res, rec(s | 1 << u, u) + t[v][u]);
		}
	}
	return dp[s][v] = res;
}

int main() {
	int m;

	cin >> n;
	cin >> m;

	for (int i = 0; i < (1 << n); i++) {
		for (int j = 0; j < n; j++) {
			dp[i][j] = -1;
		}
	}
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			t[i][j] = INF;
		}
	}

	for (int i = 0; i < m; i++) {
		int a, b, c;
		cin >> a >> b >> c;
		t[a][b] = c;
	}

	/*for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			cout << t[i][j] << " ";
		}
		cout << endl;
	}
	cout << endl;*/
	if (rec(0, 0) == INF) {
		cout << -1 << endl;
	}
	else {
		cout << rec(0, 0) << endl;
	}

	/*for (int i = 0; i < (1 << n); i++) {
		for (int j = 0; j < n; j++) {
			cout << dp[i][j] << " ";
		}
		cout << endl;
	}*/

	return 0;
}

```