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
#include <iostream>
#include <vector>
#include <cmath>
#include <cstdio>
#include <string>
#include <algorithm>
#include <map>
#include <queue>
#include <climits>
#include <bitset>
#define MOD 1000000007
// INT_MAX
using namespace std;

// struct Node
// {
// 	bitset<16> bit;
// 	// vector<int> indeg;
// 	int cur;
// 	int path;
// };

class Solver
{
private:
	int v;
	int e;
	vector<vector<int> > adj;
public:
	Solver(){
		cin >> v >> e;
		adj.resize(v);
		for (int i = 0; i < v; ++i)
		{
			adj[i].resize(v);
			for (int j = 0; j < n; ++j)
			{
				adj[i][j] = INT_MAX;
			}
		}

		for (int i = 0; i < e; ++i)
		{
			int s, t, d;
			cin >> s >> t >> d;
			adj[s][t] = d;
		}
		dp = vector<vector<int> >(1 << v, vector<int>(v, INT_MAX) );
	}

	int recursive(int bit, int cur){
		if(dp[bit][cur] != INT_MAX){
			return dp[bit][cur];
		}

		if(bit == (1 << v) - 1 && cur = 0) return 0;
		int ans = INT_MAX;
		for (int i = 0; i < v; ++i)
		{
			if(bit >> i & 0){
				ans = min(ans, recursive(bit | 1 << i, i));
			}
		}
		return dp[bit][cur] = ans; 
	}

	void exec(){
		int ans = recursive(0, 0);
		if(ans == INT_MAX) ans = -1;
		cout << ans << endl;
	}
};


int main(){
	Solver s = Solver();
	s.exec();
}