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<stdio.h>
#include<algorithm>
#include <list>
#include <stack>
#include <queue>
#include <map>
#include <vector>
#include <iostream>
#include <string>
#include <time.h>
#include <random>
#include <functional>
using namespace std;

int dp[16][16];
int V, E;
int v[16][16] = { 0 };
list<int> li;
list<int>::iterator lp;
int Max = -1;

int same(int x) {
	for (auto i = li.begin(); i != li.end();) {
		if (*i == x) return 0;
		++i;
	}
	return 1;
}a
void addsum(void) {
	int sum = 0;
	auto i = li.begin();
	auto j = i;
	++j;
	do {
		sum += v[*i][*j];
		++i; ++j;
	} while (j != li.end());
	sum += v[*i][0];
	if (sum == -1 || sum < Max) {
		Max = sum;
	}
}
void tansaku(list<int>::iterator p) {
	if (li.size() < V) {
		for (int i = 1; i < V; ++i) {
			if (*p != i && v[*p][i] != -1) {
				if (same(i)) {
					li.push_back(i);
					tansaku(++p);
					--p;
					li.pop_back();
				}
			}
		}
	}
	else {
		if (v[*p][0] != -1) {
			addsum();
		}
	}
}
int main() {
	fill(v[0], v[16], -1);
	int s, t, d;
	scanf("%d %d", &V, &E);
	for (int i = 0; i < E; ++i) {
		scanf("%d %d %d", &s, &t, &d);
		v[s][t] = d;
	}
	li.push_back(0);
	tansaku(li.begin());
	printf("%d\n", Max);
}