#include <iostream>
#include <string.h>
#include <algorithm>

using namespace std;
static const int INF = 1e9;
static const int MAX_V = 15;
int V;
int d[MAX_V][MAX_V];
int dp[1 << MAX_V][MAX_V];


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

void solve()
{
	int E;
	cin >> V >> E;
	for (int i = 0; i < V; ++i)
	{
		for (int j = 0; j < V; ++j)
		{
			d[i][j] = INF;
		}
	}
	for (int i = 0; i < E; ++i)
	{
		int s, t, cost;
		cin >> s >> t >> cost;
		d[s][t] = cost;
	}
	memset(dp, -1, sizeof(dp));
	int ans = rec(0, 0);
	if (ans == INF)
	{
		cout << -1 << endl;
	}
	else
	{
		cout << ans << endl;
	}
}

int main()
{
	solve();
	return(0);
}
### Prompt

Your challenge is to write 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 <string.h>
#include <algorithm>

using namespace std;
static const int INF = 1e9;
static const int MAX_V = 15;
int V;
int d[MAX_V][MAX_V];
int dp[1 << MAX_V][MAX_V];


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

void solve()
{
	int E;
	cin >> V >> E;
	for (int i = 0; i < V; ++i)
	{
		for (int j = 0; j < V; ++j)
		{
			d[i][j] = INF;
		}
	}
	for (int i = 0; i < E; ++i)
	{
		int s, t, cost;
		cin >> s >> t >> cost;
		d[s][t] = cost;
	}
	memset(dp, -1, sizeof(dp));
	int ans = rec(0, 0);
	if (ans == INF)
	{
		cout << -1 << endl;
	}
	else
	{
		cout << ans << endl;
	}
}

int main()
{
	solve();
	return(0);
}
```