#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pll;

ll n,e;
ll inf=1e15;
vector<vector<ll>> E(15,vector<ll>(15,inf));
vector<vector<ll>> dp(1<<15+1,vector<ll>(15,-1));

ll rec(ll s,ll bit, ll v) {
  if(dp[bit][v]!=-1) return dp[bit][v];
  if(bit==(1<<v)) return dp[bit][v]=E[s][v];
  ll res=inf;
  ll prev_bit=bit-(1<<v);
  for(ll i=0;i<n;i++) {
    if(prev_bit&(1<<i)) {
      res=min(res,rec(s,prev_bit,i)+E[i][v]);
    }
  }
  return dp[bit][v]=res;
}

int main() {
  cin >> n >> e;
  for(ll i=0;i<e;i++) {
    ll f,t,w;
    cin >> f >> t >> w;
    E[f][t]=w;
  }
  ll ans=inf;
  for(ll i=0;i<n;i++) {
    ans=min(ans,rec(i,(1<<n)-1,i));
    for(ll j=0;j<n;j++) {
      for(ll k=0;k<(1<<n);k++) {
        dp[k][j]=-1;
      }
    }
  }
  if(ans==inf) {
    ans=-1;
  }
  cout << ans << endl;
}

### Prompt

Please create a solution in CPP to 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>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pll;

ll n,e;
ll inf=1e15;
vector<vector<ll>> E(15,vector<ll>(15,inf));
vector<vector<ll>> dp(1<<15+1,vector<ll>(15,-1));

ll rec(ll s,ll bit, ll v) {
  if(dp[bit][v]!=-1) return dp[bit][v];
  if(bit==(1<<v)) return dp[bit][v]=E[s][v];
  ll res=inf;
  ll prev_bit=bit-(1<<v);
  for(ll i=0;i<n;i++) {
    if(prev_bit&(1<<i)) {
      res=min(res,rec(s,prev_bit,i)+E[i][v]);
    }
  }
  return dp[bit][v]=res;
}

int main() {
  cin >> n >> e;
  for(ll i=0;i<e;i++) {
    ll f,t,w;
    cin >> f >> t >> w;
    E[f][t]=w;
  }
  ll ans=inf;
  for(ll i=0;i<n;i++) {
    ans=min(ans,rec(i,(1<<n)-1,i));
    for(ll j=0;j<n;j++) {
      for(ll k=0;k<(1<<n);k++) {
        dp[k][j]=-1;
      }
    }
  }
  if(ans==inf) {
    ans=-1;
  }
  cout << ans << endl;
}

```