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>
using namespace std;
const int INF =
    sizeof(int) == sizeof(long long) ? 0x3f3f3f3f3f3f3f3fLL : 0x3f3f3f3f;
const int MOD = (int)(1e9) + 7;
template <class T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}
using Weight = int;
using Flow = int;
struct Edge {
  int s, d;
  Weight w;
  Flow c;
  Edge(){};
  Edge(int s, int d, Weight w = 1) : s(s), d(d), w(w), c(w){};
};
bool operator<(const Edge &e1, const Edge &e2) { return e1.w < e2.w; }
bool operator>(const Edge &e1, const Edge &e2) { return e2 < e1; }
inline ostream &operator<<(ostream &os, const Edge &e) {
  return (os << '(' << e.s << ", " << e.d << ", " << e.w << ')');
}
using Edges = vector<Edge>;
using Graph = vector<Edges>;
using Array = vector<Weight>;
using Matrix = vector<Array>;
void add_arc(Graph &g, int s, int d, Weight w = 1) {
  g[s].emplace_back(s, d, w);
}
void add_edge(Graph &g, int a, int b, Weight w = 1) {
  add_arc(g, a, b, w);
  add_arc(g, b, a, w);
}
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int V, E;
  cin >> V >> E;
  Matrix g(V, Array(V, INF));
  for (int i = (0); i < (E); i++) {
    int s, t, d;
    cin >> s >> t >> d;
    g[s][t] = d;
  }
  vector<int> p(V);
  iota(begin(p), end(p), 0);
  Weight ans = INF;
  do {
    Weight tmp = 0;
    for (int i = (0); i < (V); i++) {
      tmp += g[p[i]][p[(i + 1) % V]];
      chmin(tmp, INF);
    }
    chmin(ans, tmp);
  } while (next_permutation(begin(p), end(p)));
  cout << (ans == INF ? -1 : ans) << endl;
  return 0;
}
