#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES
//#include "MyMath.h"
//#include "MyDisjointset.h"
#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
#include <functional>
#include <stdio.h>
#include <math.h>
#include <string.h>
using namespace std;
typedef pair<int, int> P; typedef long long int ll;
const int INF = 10000000;
int n, e;
int d[15][15], dp[1 << 15][15];
int rec(int s, int v) {
	if (s == (1 << n) - 1 && v == 0) return dp[s][v] = 0;
	else if (dp[s][v] != -1) return dp[s][v];
	else {
		int res = INF;
		for (int i = 0; i < n; i++) {
			if (!(s >> i & 1)) res = min(res, d[v][i] + rec(s | 1 << i, i));
		}
		return dp[s][v] = res;
	}
}
int main() {
	cin >> n >> e;
	fill(d[0], d[15], INF);
	fill(dp[0], dp[1 << 15], -1);
	for (int i = 0; i < e; i++) {
		int s, t, dis; cin >> s >> t >> dis;
		d[s][t] = dis;
	}
	if (rec(0, 0) >= 10000000) cout << -1 << endl;
	else cout << rec(0, 0) << endl;
	return 0;
}
### Prompt

Generate 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
#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES
//#include "MyMath.h"
//#include "MyDisjointset.h"
#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
#include <functional>
#include <stdio.h>
#include <math.h>
#include <string.h>
using namespace std;
typedef pair<int, int> P; typedef long long int ll;
const int INF = 10000000;
int n, e;
int d[15][15], dp[1 << 15][15];
int rec(int s, int v) {
	if (s == (1 << n) - 1 && v == 0) return dp[s][v] = 0;
	else if (dp[s][v] != -1) return dp[s][v];
	else {
		int res = INF;
		for (int i = 0; i < n; i++) {
			if (!(s >> i & 1)) res = min(res, d[v][i] + rec(s | 1 << i, i));
		}
		return dp[s][v] = res;
	}
}
int main() {
	cin >> n >> e;
	fill(d[0], d[15], INF);
	fill(dp[0], dp[1 << 15], -1);
	for (int i = 0; i < e; i++) {
		int s, t, dis; cin >> s >> t >> dis;
		d[s][t] = dis;
	}
	if (rec(0, 0) >= 10000000) cout << -1 << endl;
	else cout << rec(0, 0) << endl;
	return 0;
}
```