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;
template <typename T>
void chmax(T &a, T b) {
  a = max(a, b);
}
template <typename T>
void chmin(T &a, T b) {
  a = min(a, b);
}
template <typename T>
void chadd(T &a, T b) {
  a = a + b;
}
long long int dx[] = {0, 0, 1, -1};
long long int dy[] = {1, -1, 0, 0};
constexpr long long INF = 1001001001001001LL;
constexpr long long MOD = 1000000007LL;
vector<pair<long long int, long long int> > G[20];
long long int dp[1 << 15][15];
void solve() {
  long long int V, E;
  cin >> V >> E;
  for (long long int(i) = (0); (i) < (E); (i)++) {
    long long int s, t, d;
    cin >> s >> t >> d;
    G[s].push_back(pair<long long int, long long int>(t, d));
  }
  long long int ans = INF;
  for (long long int(i) = (0); (i) < (1 << V); (i)++)
    for (long long int(j) = (0); (j) < (V); (j)++) dp[i][j] = INF;
  dp[0][0] = 0;
  for (long long int(bit) = (0); (bit) < (1 << V); (bit)++)
    for (long long int(i) = (0); (i) < (V); (i)++) {
      for (auto x : G[i]) {
        if (bit >> x.first & 1) continue;
        long long int nbit = bit | (1 << x.first);
        chmin(dp[nbit][x.first], dp[bit][i] + x.second);
      }
    }
  for (long long int(i) = (0); (i) < (V); (i)++)
    chmin(ans, dp[(1 << V) - 1][i]);
  cout << (ans == INF ? -1 : ans) << endl;
}
signed main() {
  solve();
  return 0;
}
