#include "bits/stdc++.h"

using namespace std;

int V, E, o;
int dis[16][16], dp[16][1<<16];

int solve(int s, int state)
{
	if (~dp[s][state])
	{
		return dp[s][state];
	}
	if (state == (1<<V)-1)
	{
		return dp[s][state] = dis[s][o];
	}
	int res = INT_MAX;
	for (int i = 0; i < V; i++)
	{
		if (state >> i & 1) continue;
		res = min(res, solve(i, state | 1 << i) + dis[s][i]);
	}
	return dp[s][state] = res;
}

int main()
{
	cin >> V >> E;
	memset(dis, -1, sizeof(dis));
	while(E--)
	{
		int s, t, w;
		cin >> s >> t >> w;
		dis[s][t] = w;
	}
	for (int s = 0; s < V; s++)
	{
		for (int t = 0; t < V; t++)
		{
			if (dis[s][t] == -1)
			{
				dis[s][t] = 1000000;
			}
		}
	}
	int ans = INT_MAX;
	for (int s = 0; s < V; s++)
	{
		o = s;
		memset(dp, -1, sizeof(dp));
		ans = min(ans, solve(s, 1<<s));
	}
	if (ans > 1000000)
	{
		ans = -1;
	}
	cout << ans << endl;
	//cout << "yui(*-v・)yui" << endl;
	return 0;
}


### Prompt

Please create a solution in Cpp 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;

int V, E, o;
int dis[16][16], dp[16][1<<16];

int solve(int s, int state)
{
	if (~dp[s][state])
	{
		return dp[s][state];
	}
	if (state == (1<<V)-1)
	{
		return dp[s][state] = dis[s][o];
	}
	int res = INT_MAX;
	for (int i = 0; i < V; i++)
	{
		if (state >> i & 1) continue;
		res = min(res, solve(i, state | 1 << i) + dis[s][i]);
	}
	return dp[s][state] = res;
}

int main()
{
	cin >> V >> E;
	memset(dis, -1, sizeof(dis));
	while(E--)
	{
		int s, t, w;
		cin >> s >> t >> w;
		dis[s][t] = w;
	}
	for (int s = 0; s < V; s++)
	{
		for (int t = 0; t < V; t++)
		{
			if (dis[s][t] == -1)
			{
				dis[s][t] = 1000000;
			}
		}
	}
	int ans = INT_MAX;
	for (int s = 0; s < V; s++)
	{
		o = s;
		memset(dp, -1, sizeof(dp));
		ans = min(ans, solve(s, 1<<s));
	}
	if (ans > 1000000)
	{
		ans = -1;
	}
	cout << ans << endl;
	//cout << "yui(*-v・)yui" << endl;
	return 0;
}


```