#include "bits/stdc++.h"
#include "math.h"
 
using namespace std;
typedef long long ll;
typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vector<int> vin;
typedef pair<ll,ll> P;
typedef vector<P> vp;
#define rep(i,a,b) for(ll i=(a);i<(b);++i)
#define drep(i,a,b) for(ll i=(a);i>=(b);--i)
#define SIZE(a) int((a).size())
#define out(a) cout<<(a)<<endl;
const int INF=INT_MAX;
const int MAX = 510000;
const ll MOD = 10000;
ll fac[MAX], finv[MAX], inv[MAX];

int main(){
  ll v,e;cin>>v>>e;
  vvll g(v,vll(v,INF)),dp(1<<v,vll(v,INF));
  rep(i,0,e){
    ll s,t,d;cin>>s>>t>>d;
    g[s][t]=d;
  }
  dp[(1<<v)-1][0]=0;
  drep(s,(1<<v)-2,0){
    rep(i,0,v){
      rep(j,0,v){
        if(!(s>>j&1)){
          dp[s][i]=min(dp[s][i],dp[s|1<<j][j]+g[i][j]);
        }
      }
    }
  }
  cout<<(dp[0][0]==INF?-1:dp[0][0])<<endl;
}


### Prompt

Create a solution in cpp for the following problem:

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

### Response

```cpp
#include "bits/stdc++.h"
#include "math.h"
 
using namespace std;
typedef long long ll;
typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vector<int> vin;
typedef pair<ll,ll> P;
typedef vector<P> vp;
#define rep(i,a,b) for(ll i=(a);i<(b);++i)
#define drep(i,a,b) for(ll i=(a);i>=(b);--i)
#define SIZE(a) int((a).size())
#define out(a) cout<<(a)<<endl;
const int INF=INT_MAX;
const int MAX = 510000;
const ll MOD = 10000;
ll fac[MAX], finv[MAX], inv[MAX];

int main(){
  ll v,e;cin>>v>>e;
  vvll g(v,vll(v,INF)),dp(1<<v,vll(v,INF));
  rep(i,0,e){
    ll s,t,d;cin>>s>>t>>d;
    g[s][t]=d;
  }
  dp[(1<<v)-1][0]=0;
  drep(s,(1<<v)-2,0){
    rep(i,0,v){
      rep(j,0,v){
        if(!(s>>j&1)){
          dp[s][i]=min(dp[s][i],dp[s|1<<j][j]+g[i][j]);
        }
      }
    }
  }
  cout<<(dp[0][0]==INF?-1:dp[0][0])<<endl;
}


```