#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
#define REP(i,n) for(int i=1;i<=n;i++)
typedef long long ll;

struct edge{
	int to;
	int cost;
};

vector<edge> to[20];
int dp[40000][20];
const int INF = 1001001001;

int main(){
	int v,e;
	cin >> v >> e;
	
	rep(i,e){
		int s,t,d;
		cin >> s >> t >> d;
		to[s].push_back(edge{t,d});
	}
	
	int ans = INF;

	rep(i,v){
		rep(i,1<<v){
			rep(j,v){
				dp[i][j] = INF;
			}
		}
		dp[1<<i][i] = 0;
		rep(s, 1<<v){
			rep(j, v){
				if(!(s & (1<<j))) continue;
				for(auto nextv: to[j]){
					if(s == (1<<v)-1 && nextv.to == i){
						ans = min(ans, dp[s][j] + nextv.cost);
					}
					if(s & (1<<nextv.to)) continue;
					dp[s | (1<<nextv.to)][nextv.to] = min(dp[s | (1<<nextv.to)][nextv.to], dp[s][j] + nextv.cost);
				}
			}
		}
	}
	
	if(ans == INF) ans = -1;
	cout << ans << endl;
	
	return 0;
}



### Prompt

In CPP, your task is to solve 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;
#define rep(i,n) for(int i=0;i<n;i++)
#define REP(i,n) for(int i=1;i<=n;i++)
typedef long long ll;

struct edge{
	int to;
	int cost;
};

vector<edge> to[20];
int dp[40000][20];
const int INF = 1001001001;

int main(){
	int v,e;
	cin >> v >> e;
	
	rep(i,e){
		int s,t,d;
		cin >> s >> t >> d;
		to[s].push_back(edge{t,d});
	}
	
	int ans = INF;

	rep(i,v){
		rep(i,1<<v){
			rep(j,v){
				dp[i][j] = INF;
			}
		}
		dp[1<<i][i] = 0;
		rep(s, 1<<v){
			rep(j, v){
				if(!(s & (1<<j))) continue;
				for(auto nextv: to[j]){
					if(s == (1<<v)-1 && nextv.to == i){
						ans = min(ans, dp[s][j] + nextv.cost);
					}
					if(s & (1<<nextv.to)) continue;
					dp[s | (1<<nextv.to)][nextv.to] = min(dp[s | (1<<nextv.to)][nextv.to], dp[s][j] + nextv.cost);
				}
			}
		}
	}
	
	if(ans == INF) ans = -1;
	cout << ans << endl;
	
	return 0;
}



```