#include<iostream>
#include<algorithm>
using namespace std;

#define MAX_N 18
#define INF 1000000000
int N, M, a, b, c, x[MAX_N][MAX_N];
int dp[MAX_N][1 << MAX_N];

int main() {
	for (int i = 0; i < MAX_N; i++) {
		for (int j = 0; j < MAX_N; j++) { x[i][j] = INF; }
		for (int j = 0; j < (1 << MAX_N); j++) { dp[i][j] = INF; }
	
	}
	cin >> N >> M;
	for (int i = 0; i < M; i++) {
		cin >> a >> b >> c;
		x[a][b] = c;
	}
	dp[0][1] = 0;
	for (int i = 0; i < (1 << N); i++) {
		for (int j = 0; j < N; j++) {
			if (dp[j][i] < INF) {
				for (int k = 0; k < N; k++) {
					if ((i / (1 << k)) % 2 == 0) {
						int dist1 = dp[j][i] + x[j][k];
						int pos = i + (1 << k);
						if (dp[k][pos] > dist1) {
							dp[k][pos] = dist1;
						}
					}
				}
			}
		}
	}
	int maxn = INF;
	for (int i = 0; i < N; i++) {
		maxn = min(dp[i][(1 << N) - 1] + x[i][0], maxn);
	}
	if (maxn == INF) { maxn = -1; }
	cout << maxn << 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
#include<iostream>
#include<algorithm>
using namespace std;

#define MAX_N 18
#define INF 1000000000
int N, M, a, b, c, x[MAX_N][MAX_N];
int dp[MAX_N][1 << MAX_N];

int main() {
	for (int i = 0; i < MAX_N; i++) {
		for (int j = 0; j < MAX_N; j++) { x[i][j] = INF; }
		for (int j = 0; j < (1 << MAX_N); j++) { dp[i][j] = INF; }
	
	}
	cin >> N >> M;
	for (int i = 0; i < M; i++) {
		cin >> a >> b >> c;
		x[a][b] = c;
	}
	dp[0][1] = 0;
	for (int i = 0; i < (1 << N); i++) {
		for (int j = 0; j < N; j++) {
			if (dp[j][i] < INF) {
				for (int k = 0; k < N; k++) {
					if ((i / (1 << k)) % 2 == 0) {
						int dist1 = dp[j][i] + x[j][k];
						int pos = i + (1 << k);
						if (dp[k][pos] > dist1) {
							dp[k][pos] = dist1;
						}
					}
				}
			}
		}
	}
	int maxn = INF;
	for (int i = 0; i < N; i++) {
		maxn = min(dp[i][(1 << N) - 1] + x[i][0], maxn);
	}
	if (maxn == INF) { maxn = -1; }
	cout << maxn << endl;
	return 0;
}
```