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

const int INF = 1e9;
const int MAX_V = 16;
const int MAX_S = 1 << 16;

int V,E;
int dist[MAX_V][MAX_V];
int dp[MAX_S][MAX_V];

void chmin(int &a, int b){ if( a > b){ swap(a,b);} return ;}

int rec(int S, int a){
  if( dp[S][a] >= 0){ return dp[S][a];}
  if( S == (1<<V)-1 && a == 0){ return 0;}
  
  int res = INF;
  for(int u = 0; u < V; u++){
    if( !(( S >> u) & 1)){//まだuに未到達
      chmin(res, rec(S|(1<<u),u)+dist[a][u]);}}
   
  return dp[S][a] = res;
}
                             
      
    

int main(){
 scanf("%d",&V); scanf("%d",&E);
 
  
  for(int i = 0; i < MAX_V; i++){
    for(int j = 0; j < MAX_V; j++){
      dist[i][j] = INF;}}
  //繋がっていない状態をINFとする
  for(int i = 0; i < MAX_S; i++){
    for(int j = 0; j < MAX_V; j++){ 
      dp[i][j] = -1;}}
 
  //未更新を-1とする
  while(E--){
    int s,t,d; cin >> s >> t >> d; dist[s][t] = d;}
  
  if( rec(0,0) != INF){ printf("%d\n", rec(0,0)); }
  else{ printf("%d\n", -1) ;}return 0;}
  
  

### Prompt

Please provide a Cpp coded solution to the problem described below:

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;

const int INF = 1e9;
const int MAX_V = 16;
const int MAX_S = 1 << 16;

int V,E;
int dist[MAX_V][MAX_V];
int dp[MAX_S][MAX_V];

void chmin(int &a, int b){ if( a > b){ swap(a,b);} return ;}

int rec(int S, int a){
  if( dp[S][a] >= 0){ return dp[S][a];}
  if( S == (1<<V)-1 && a == 0){ return 0;}
  
  int res = INF;
  for(int u = 0; u < V; u++){
    if( !(( S >> u) & 1)){//まだuに未到達
      chmin(res, rec(S|(1<<u),u)+dist[a][u]);}}
   
  return dp[S][a] = res;
}
                             
      
    

int main(){
 scanf("%d",&V); scanf("%d",&E);
 
  
  for(int i = 0; i < MAX_V; i++){
    for(int j = 0; j < MAX_V; j++){
      dist[i][j] = INF;}}
  //繋がっていない状態をINFとする
  for(int i = 0; i < MAX_S; i++){
    for(int j = 0; j < MAX_V; j++){ 
      dp[i][j] = -1;}}
 
  //未更新を-1とする
  while(E--){
    int s,t,d; cin >> s >> t >> d; dist[s][t] = d;}
  
  if( rec(0,0) != INF){ printf("%d\n", rec(0,0)); }
  else{ printf("%d\n", -1) ;}return 0;}
  
  

```