#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define REP(i,n) FOR(i,0,n)
#define FOR(i,a,b) for(ll i=a;i<b;i++)
#define PB push_back
#define LB lower_bound
#define UB upper_bound
#define PQ priority_queue
#define UM unordered_map
#define ALL(a) (a).begin(),(a).end()
typedef vector<ll> vi;
typedef vector<vector<ll>> vvi;
const ll INF = (1ll << 60);
typedef pair<ll,ll> pii;
struct Edge {ll s,t,d;};
typedef vector<vector<Edge>> Graph;

int main(){
  ll V,E; cin>>V>>E;
  Graph G(V);
  REP(i,E) {Edge e; cin>>e.s>>e.t>>e.d; G[e.t].PB(e);}
  vvi dist((1ll<<V),vi(V,INF));
  dist[1][0]=0;

  FOR(i,2,(1ll<<V)) REP(j,V) {
    if((1ll<<j)&i) for(Edge e:G[j]) dist[i][j]=min(dist[i][j],dist[(1ll<<j)^i][e.s]+e.d);
  }

  ll ans=INF;
  for(Edge e:G[0]) ans=min(ans,dist[(1ll<<V)-1][e.s]+e.d);
  if(ans==INF) ans=-1;
  cout<<ans<<endl;
}
### Prompt

Your challenge is to write a CPP solution 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;
#define REP(i,n) FOR(i,0,n)
#define FOR(i,a,b) for(ll i=a;i<b;i++)
#define PB push_back
#define LB lower_bound
#define UB upper_bound
#define PQ priority_queue
#define UM unordered_map
#define ALL(a) (a).begin(),(a).end()
typedef vector<ll> vi;
typedef vector<vector<ll>> vvi;
const ll INF = (1ll << 60);
typedef pair<ll,ll> pii;
struct Edge {ll s,t,d;};
typedef vector<vector<Edge>> Graph;

int main(){
  ll V,E; cin>>V>>E;
  Graph G(V);
  REP(i,E) {Edge e; cin>>e.s>>e.t>>e.d; G[e.t].PB(e);}
  vvi dist((1ll<<V),vi(V,INF));
  dist[1][0]=0;

  FOR(i,2,(1ll<<V)) REP(j,V) {
    if((1ll<<j)&i) for(Edge e:G[j]) dist[i][j]=min(dist[i][j],dist[(1ll<<j)^i][e.s]+e.d);
  }

  ll ans=INF;
  for(Edge e:G[0]) ans=min(ans,dist[(1ll<<V)-1][e.s]+e.d);
  if(ans==INF) ans=-1;
  cout<<ans<<endl;
}
```