#include <bits/stdc++.h>
using namespace std;
const int N=100010;
int t,n,m,k,tot=0,head[N*2],nxt[N*2],idx[N*2],va[N],b[N],vis[N],a[N];
long long val[N*2],dis[N],mi=1e18;
void add(int x,int y,long long z)
{
    idx[++tot]=y;
    val[tot]=z;
    nxt[tot]=head[x];
    head[x]=tot;
}
void dijstra(int s)
{
    for (int i=1;i<=n;i++)
	{
		dis[i]=1e18;
		vis[i]=0;
	}
	priority_queue<pair<long long,int>,vector<pair<long long,int>>,greater<pair<long long,int>>> q;
    dis[s]=0;
    q.push(make_pair(0,s));
    while (!q.empty())
    {
		int t=q.top().second; q.pop();
	    if (vis[t]) continue;
	    vis[t]=1;
	    for (int i=head[t];i;i=nxt[i])
	    {
		    int y=idx[i];
		    //if (vis[y]) continue;
		    if (dis[y]>dis[t]+val[i])
		    {
			    dis[y]=dis[t]+val[i];	
				q.push(make_pair(dis[y],y));
			}
		}
	}
}
int main() {
	freopen("WAW.in","r",stdin);
	freopen("WAW.out","w",stdout); 
    scanf("%d",&t);
	while (t--)
    {
	    tot=0,mi=1e18;
		scanf("%d%d%d",&n,&m,&k);
		memset(head,0,sizeof(head));
	    for (int i=1;i<=m;i++)
	    {
			int x,y;
			long long z;
		    scanf("%d%d%lld",&x,&y,&z);
		    add(x,y,z);
		}
		for (int i=1;i<=k;i++)
		{
		    scanf("%d",&a[i]);
		    b[a[i]]=1;
		}
		for (int i=1;i<=k;i++)
		{
		    dijstra(a[i]);
		    for (int j=1;j<=k;j++)
		    {
				if (i==j) continue;
				mi=min(mi,dis[a[j]]);
			}
		}
		printf("%lld\n",mi);
	}
}