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<bits/stdc++.h>
#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cstdlib>
using namespace std;

#define now dp[st][pos][bits]

const int N = 16, INF = 0x3f3f3f3f;

int n, m, end;
int G[N + 5][N + 5];
int dp[N][N][1 << N];
//dp i,j,k ??¨??????i????????????????????¨j????????????????????¶??????k??¶????????°?????????????°???????
//??¨??????????????¶??????????????¶????§???????0??????????????¶????????\??¨???????????\

inline int nextInt(void) {
	int res;
	scanf("%d", &res);
	return res;
}

inline void addEdge(int x, int y, int w) {
	G[x][y] = w;
}

inline void makeEnd(void) {
	end = 0;
	for (int i = 0; i < n; i++)
		end |= (1 << i);
}

int DP(int st, int pos, int bits) {
	//cout << "Searching for DP " << st << " " << pos << " " << bits << endl;
	if (~now)	//??°??????????´¢
		return now;
	if (st == pos&&bits == end)	//???????????°??????????????????????????????
		return now = 0;
	now = INF;
	for (int i = 0; i < n; i++)	//????????????
		if (i != pos &&!( (bits >> i) & 1))	//?????????????\??????????
			now = min(now, DP(st, i, bits | (1 << i)) + G[pos][i]);
	//cout << "Found DP " << st << " " << pos << " " << bits << " = " << now << endl;
	return now;
}

signed main(void) {
	memset(G, 0x3f, sizeof(G));
	memset(dp, -1, sizeof(dp));
	n = nextInt();
	m = nextInt();
	for (int i = 0; i < m; i++) {
		int x = nextInt();
		int y = nextInt();
		int w = nextInt();
		addEdge(x, y, w);
	}
	makeEnd();
	int ans = INF;
	for (int i = 0; i < n; i++)
		ans = min(ans, DP(i, i, 0));
	printf("%d\n", ans < INF ? ans : -1);
}