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
//============================================================================
// Name        : dpl_2a.cpp
// Author      : afterCmidday
// Version     :
// Copyright   : Your copyright notice
// Description : Hello World in C++, Ansi-style
//============================================================================

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

int main() {
	int edge[15][15], v, e, dp[15][1 << 15];
	cin >> v >> e;
	memset(edge,-1,sizeof(edge));
	memset(dp,-1,sizeof(dp));
	for(int i = 0;i < v;i++){
		dp[i][0] = 0;
	}
	for(int i = 0;i < e;i++){
		int s, t, d;
		cin >> s >> t >> d;
		edge[s][t] = d;
	}
	for(int i = 0;i < (1 << v);i++){
		for(int j = 0;j < v;j++){ // now place
			if(dp[j][i] != -1){
				for(int k = 0;k < v;k++){ // next place
					if((i >> k & 1) == 0 && edge[j][k] != -1 && (dp[k][i | (1 << k)] == -1 || dp[k][i | (1 << k)] < dp[j][i] + edge[j][k])){
						dp[k][i | (1 << k)] = dp[j][i] + edge[j][k];
					}
				}
			}
		}
	}
	int ans = -1;
	for(int i = 0;i < v;i++){
		if(dp[i][(1 << v) - 1] != -1 && (ans == -1 || dp[i][(1 << v) - 1] < ans){
			ans = dp[i][(1 << v) - 1];
		}
	}
	cout << ans << endl;
	return 0;
}