#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int INF = 1e9;
int v,e;
int g[15][15];
int dp[1<<15][15];

void dfs(int idx,int bit)
{
	for(int i = 0;i<v;i++)
	{
		 if((bit&(1<<i))==0)
		 {
			 //cout<<i<<endl;
			 if(g[idx][i]!=-1)
			 {
				if(dp[bit|(1<<i)][i]>dp[bit][idx]+g[idx][i])
			 	{
					 dp[bit|(1<<i)][i] = dp[bit][idx]+g[idx][i];
				 dfs(i,bit|(1<<i));
				 }
			 }
		 }
	}
}

int main()
{
	cin >> v >> e;
	for(int i = 0 ;i<15;i++)
	{
		for(int j = 0;j<15;j++)
		{
			g[i][j] = -1;
		}
	}
	for(int i = 0;i<(1<<15);i++)
	{
		for(int j = 0;j < 15;j++)
		{
			dp[i][j] = INF;
		}
	}
	for(int i = 0;i<e;i++)
	{
		int fr,to,cost;
		cin >> fr >> to >> cost;
		fr;
		to;
		g[fr][to] = cost;
	}
	dp[0][0] = 0;
	dfs(0,0);
	int ans = INF;
	for(int i = 0;i<v;i++){ans = min(ans,dp[(1<<v)-1][0]);}
	//for(int i = 0;i<(1<<v);i++){for(int j = 0;j<v;j++){cout<<dp[i][j]<<' ';}cout<<endl;}
	cout<<(ans==INF?-1:ans)<<endl;
	return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

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;
typedef long long ll;
const int INF = 1e9;
int v,e;
int g[15][15];
int dp[1<<15][15];

void dfs(int idx,int bit)
{
	for(int i = 0;i<v;i++)
	{
		 if((bit&(1<<i))==0)
		 {
			 //cout<<i<<endl;
			 if(g[idx][i]!=-1)
			 {
				if(dp[bit|(1<<i)][i]>dp[bit][idx]+g[idx][i])
			 	{
					 dp[bit|(1<<i)][i] = dp[bit][idx]+g[idx][i];
				 dfs(i,bit|(1<<i));
				 }
			 }
		 }
	}
}

int main()
{
	cin >> v >> e;
	for(int i = 0 ;i<15;i++)
	{
		for(int j = 0;j<15;j++)
		{
			g[i][j] = -1;
		}
	}
	for(int i = 0;i<(1<<15);i++)
	{
		for(int j = 0;j < 15;j++)
		{
			dp[i][j] = INF;
		}
	}
	for(int i = 0;i<e;i++)
	{
		int fr,to,cost;
		cin >> fr >> to >> cost;
		fr;
		to;
		g[fr][to] = cost;
	}
	dp[0][0] = 0;
	dfs(0,0);
	int ans = INF;
	for(int i = 0;i<v;i++){ans = min(ans,dp[(1<<v)-1][0]);}
	//for(int i = 0;i<(1<<v);i++){for(int j = 0;j<v;j++){cout<<dp[i][j]<<' ';}cout<<endl;}
	cout<<(ans==INF?-1:ans)<<endl;
	return 0;
}

```