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>
#define int long long int
#define MOD(x) ((x % MOD_N) + MOD_N) % MOD_N
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define FORE(i,a,b) for(int i=(a);i<=(b);++i)
#define RFOR(i,a,b) for(int i=(b)-1;i>=(a);--i)
#define RFORE(i,a,b) for(int i=(b);i>=(a);--i)
#define REP(i,n) FOR(i,0,n)
#define RREP(i,n) RFOR(i,0,n)
#define ALL(c) (c).begin(),(c).end()
#define RALL(c) (c).rbegin(),(c).rend()
#define SORT(c) sort(ALL(c))
#define RSORT(c) sort(RALL(c))
#define SZ(c) (int)((c).size())
#define EACH(i,v) for(auto i=v.begin();i!=v.end();++i)
#define REACH(i,v) for(auto i=v.rbegin();i!=v.rend();++i)
#define LB(c,x) distance((c).begin(),lower_bound(ALL(c),x))
#define UB(c,x) distance((c).begin(),upper_bound(ALL(c),x))
#define COUNT(c,x) (lower_bound(ALL(c),x)-upper_bound(ALL(c),x))
#define UNIQUE(c) SORT(c); (c).erase(unique(ALL(c)),(c).end());
#define COPY(c1,c2) copy(ALL(c1),(c2).begin())
#define EXIST(s,e) (bool)((s).find(e)!=(s).end())
#define PB push_back
#define MP make_pair
#define DUMP(x)  cerr<<#x<<" = "<<(x)<<endl;
#define NL cerr<<endl;
using namespace std;
template<typename T,typename U> using P=pair<T,U>;
template<typename T> using V=vector<T>;
template<typename T>bool chmax(T&a,T b){if(a<b){a=b;return true;}return false;}
template<typename T>bool chmin(T&a,T b){if(a>b){a=b;return true;}return false;}
template<typename T>T sum(vector<T>&v){return accumulate(ALL(v),T());}
template<typename T>T sum(vector<T>&v,int a,int b){return accumulate(v.begin()+a,v.begin()+b,T());}
template<typename T>T max(vector<T>&v){return *max_element(ALL(v));}
template<typename T>T min(vector<T>&v){return *max_element(ALL(v));}
template<typename T>T max_index(vector<T>&v){return distance((v).begin(),max_element(ALL(v)));}
template<typename T>T min_index(vector<T>&v){return distance((v).begin(),min_element(ALL(v)));}

struct edge { int to, cost; };

template<typename T>auto&operator<<(ostream&s,const vector<T>&v){s<<"[";bool a=1;for(auto e:v){s<<(a?"":" ")<<e;a=0;}s<<"]";return s;}
template<typename T,typename U>auto&operator<<(ostream&s,const pair<T,U>&p){s<<"("<<p.first<<","<<p.second<<")";return s;}
template<typename T>auto&operator<<(ostream&s,const set<T>&st){s<<"{";bool a=1;for(auto e:st){s<<(a?"":" ")<<e;a=0;}s<<"}";return s;}
template<typename T,typename U>auto&operator<<(ostream&s,const map<T,U>&m){s<<"{";bool a=1;for(auto e:m){s<<(a?"":" ")<<e.first<<":"<<e.second;a=0;}s<<"}";return s;}

const int INF = 1e3;
const int MOD_N = 1e9+7;

signed main()
{
   int n, m; cin >> n >> m;
   V<V<int>> A(n, V<int>(n, INF));
   REP(i, m) {
      int s, t, d; cin >> s >> t >> d;
      A[s][t] = d;
   }

   V<V<V<int>>> dp(n, V<V<int>>(1<<n, V<int>(n, INF)));
   REP(k, n) {
      dp[k][0][k] = 0;
      REP(s, 1<<n) {
         REP(i, n) {
            REP(j, n) if (!(s >> j & 1)) {
               chmin(dp[k][s | 1<<j][j], dp[k][s][i] + A[i][j]);
            }
         }
      }
   }
   int ans = INF;
   REP(k, n) {
      chmin(ans, dp[k][(1<<n)-1][k]);
   }
   cout << ans << endl;

   return 0;
}

