Problem:
Score : 400 points

Problem Statement

There are N towns in the State of Atcoder, connected by M bidirectional roads.

The i-th road connects Town A_i and B_i and has a length of C_i.

Joisino is visiting R towns in the state, r_1,r_2,..,r_R (not necessarily in this order).

She will fly to the first town she visits, and fly back from the last town she visits, but for the rest of the trip she will have to travel by road.

If she visits the towns in the order that minimizes the distance traveled by road, what will that distance be?

Constraints

2≤N≤200

1≤M≤N×(N-1)/2

2≤R≤min(8,N) (min(8,N) is the smaller of 8 and N.)

r_i≠r_j (i≠j)

1≤A_i,B_i≤N, A_i≠B_i

(A_i,B_i)≠(A_j,B_j),(A_i,B_i)≠(B_j,A_j) (i≠j)

1≤C_i≤100000

Every town can be reached from every town by road.

All input values are integers.

Input

Input is given from Standard Input in the following format:

N M R
r_1 ... r_R
A_1 B_1 C_1
:
A_M B_M C_M

Output

Print the distance traveled by road if Joisino visits the towns in the order that minimizes it.

Sample Input 1

3 3 3
1 2 3
1 2 1
2 3 1
3 1 4

Sample Output 1

2

For example, if she visits the towns in the order of 1, 2, 3, the distance traveled will be 2, which is the minimum possible.

Sample Input 2

3 3 2
1 3
2 3 2
1 3 6
1 2 2

Sample Output 2

4

The shortest distance between Towns 1 and 3 is 4. Thus, whether she visits Town 1 or 3 first, the distance traveled will be 4.

Sample Input 3

4 6 3
2 3 4
1 2 4
2 3 3
4 3 1
1 4 1
4 2 2
3 1 6

Sample Output 3

3

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

// debug for https://beta.atcoder.jp/contests/abc073/submissions/1583069

//set many funcs
#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#define inf 1145141919
#define llinf 1145141919810364364
#define mod 1000000007

int max(int a,int b){if(a>b){return a;}return b;}
int min(int a,int b){if(a<b){return a;}return b;}
int zt(int a,int b){return max(a,b)-min(a,b);}
int round(int a,int b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
int ceil(int a,int b){if(a%b==0){return a/b;}return (a/b)+1;}
int gcd(int a,int b){int c;while(b!=0){c=a%b;a=b;b=c;}return a;}
int lcm(int a,int b){int c=gcd(a,b);a/=c;return a*b;}
int nCr(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
int fact(int a){int i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
int pow(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
long long llmax(long long a,long long b){if(a>b){return a;}return b;}
long long llmin(long long a,long long b){if(a<b){return a;}return b;}
long long llround(long long a,long long b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
long long llceil(long long a,long long b){if(a%b==0){return a/b;}return (a/b)+1;}
long long llgcd(long long a,long long b){long long c;while(b!=0){c=a%b;a=b;b=c;}return a;}
long long lllcm(long long a,long long b){long long c=llgcd(a,b);a/=c;return a*b;}
long long llnCr(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
long long llfact(long long a){long long i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
long long llpow(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
double dbmax(double a,double b){if(a>b){return a;}return b;}
double dbmin(double a,double b){if(a<b){return a;}return b;}
int sortfncsj(const void *a,const void *b){if(*(int *)a>*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int sortfnckj(const void *a,const void *b){if(*(int *)a<*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int llsortfncsj(const void *a,const void *b){if(*(long long *)a>*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int llsortfnckj(const void *a,const void *b){if(*(long long *)a<*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int dbsortfncsj(const void *a,const void *b){if(*(double *)a>*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int dbsortfnckj(const void *a,const void *b){if(*(double *)a<*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}

long long dfs(long long np,long long tf[16],long long rk,long long cr[16][16],long long nc,long long* ans){
    long long i=0,j,f=1,dr,stf[16]={0};
    while(1){
        i++;if(i>rk){break;}
        if(tf[i] == 0){
            f=0;
            tf[i]=1;
            dr=dfs(i,tf,rk,cr,nc+cr[np][i],ans);
            tf[i]=0;
        }
    }
    if(f==1){*ans=min(*ans,nc);}
    return 0;
}

int main(void){
    long long dr,n,m,r,rl[16],i,j,k,w[256][256],a,b,c,rw[16][16],tf[16]={0},zr,res;
    scanf("%lld%lld%lld",&n,&m,&r);
    for(i=1;i<=r;i++){scanf("%lld",&rl[i]);}
    for(i=1;i<=n;i++)for(j=1;j<=n;j++)w[i][j]=inf>>1; // added
    for(i=1;i<=m;i++){
        scanf("%lld%lld%lld",&a,&b,&c);
        /*w[a][b]=c;w[b][a]=c;*/w[a][b]=w[b][a]=min(w[a][b],c); // changed
    }
    for(i=1;i<=n;i++){w[i][i]=0;}
    for(k=1;k<=n;k++){
        for(i=1;i<=n;i++){
            for(j=1;j<=n;j++){
                w[i][j]=min(w[i][j],w[i][k]+w[k][j]);
            }
        }
    }
    for(i=1;i<=8;i++){
        for(j=1;j<=8;j++){
            if(i>r||j>r){rw[i][j]=inf;}
            else{rw[i][j]=w[rl[i]][rl[j]];}
        }
    }
    res=inf;
    for(i=1;i<=r;i++){
        for(j=0;j<=15;j++){tf[j]=0;}
        zr=inf;
        tf[i]=1;
        dr = dfs(i,tf,r,rw,0,&zr);
        res=llmin(zr,res);
    }
    printf("%lld\n",res);
    return 0;
}