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 <cstdio>
#include <vector>
#include <algorithm>

using namespace std;

using Weight=long long;
static const Weight INF=1LL<<57;

struct Edge {
    size_t src, dst;
    Weight weight;
    Edge() {}
    Edge(size_t src, size_t dst, Weight weight=1):
        src(src), dst(dst), weight(weight)
    {}
};

bool operator<(const Edge &e, const Edge &f) {
    if (e.weight != f.weight) {
        return e.weight > f.weight;
    } else {
        return e.src!=f.src? e.src<f.src : e.dst<f.dst;
    }
}

using Edges=vector<Edge>;
using Vertex=vector<Edge>;
using Graph=vector<Vertex>;

void join(Graph &g, size_t s, size_t d, Weight w=1) {
    // non-directed
    g[s].push_back(Edge(s, d, w));
    g[d].push_back(Edge(d, s, w));
}

void connect(Graph &g, size_t s, size_t d, Weight w=1) {
    // directed
    g[s].push_back(Edge(s, d, w));
}

Weight travel_salesman(const Graph &g) {
    size_t V=g.size();
    vector<vector<size_t>> dp(1<<V, vector<size_t>(V, INF));
    dp[(1<<V)-1][0] = 0;

    for (size_t s=(1<<V)-2; ~s; --s)
        for (size_t v=0; v<V; ++v)
            for (const Edge &e: g[v]) {
                size_t u=e.dst;
                if (!(1<<u & s))
                    dp[s][v] = min(dp[s][v], dp[1<<u|s][u]+e.weight);
            }

    return dp[0][0]<INF? dp[0][0]:-1;
}

int main() {
    size_t V, E;
    scanf("%zu %zu", &V, &E);

    Graph g(V);
    for (size_t i=0; i<E; ++i) {
        size_t s, t;
        Weight d;
        scanf("%zu %zu %lld", &s, &t, &d);

        connect(g, s, t, d);
    }

    printf("%lld\n", travel_salesman(g));
    return 0;
}