#include <bits/stdc++.h>
using namespace std;
const int nx=1e5+5, inf=1e9;
int n, m, k, u, v, w, ans=inf, mn[nx], hd[nx];
vector<int> s, tmp;
vector<pair<int, int>> d[nx];
pair<int, int> mx1={inf, 0}, smx1={inf, 0}, mx2={inf, 0}, smx2={inf, 0};
pair<int, pair<int, int>> solve(vector<int> &x)
{
pair<int, pair<int, int>> res={inf, {0, 0}};
vector<pair<int, int>> cur={{0, x.size()-1}};
while (!cur.empty())
{
vector<pair<int, int>> nw;
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
for (int i=1; i<=n; i++) mn[i]=inf, hd[i]=i;
for (auto [l, r]:cur)
{
int md=(l+r)/2;
for (int i=l; i<=md; i++) mn[x[i]]=0, pq.push({0, x[i]});
if (l!=md) nw.push_back({l, md});
if (md+1!=r) nw.push_back({md+1, r});
}
while (!pq.empty())
{
auto [cw, u]=pq.top();
pq.pop();
if (mn[u]<cw) continue;
for (auto [v, w]:d[u]) if (mn[v]>cw+w) mn[v]=cw+w, hd[v]=hd[u], pq.push({mn[v], v});
}
for (auto i:x) if (mn[i]!=0) res=min(res, {mn[i], {i, hd[i]}});
cur=nw;
}
return res;
}
void dijkstra(int st)
{
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
for (int i=1; i<=n; i++) mn[i]=inf;
mn[st]=0;
pq.push({0, st});
while (!pq.empty())
{
auto [cw, u]=pq.top();
pq.pop();
if (mn[u]<cw) continue;
for (auto [v, w]:d[u]) if (mn[v]>cw+w) mn[v]=cw+w, pq.push({mn[v], v});
}
}
int main()
{
cin.tie(NULL)->sync_with_stdio(false);
cin>>n>>m>>k;
for (int i=1; i<=m; i++) cin>>u>>v>>w, d[u].push_back({v, w}), d[v].push_back({u, w});
for (int i=1; i<=k; i++) cin>>u, s.push_back(u);
auto [mndist, node]=solve(s);
for (auto u:s) if (u!=node.first&&u!=node.second) tmp.push_back(u);
ans=mndist+solve(tmp).first;
dijkstra(node.first);
for (auto u:s)
{
if (u==node.first||u==node.second||mn[u]==inf) continue;
if (mn[u]<mx1.first) swap(mx1, smx1), mx1={mn[u], u};
else if (mn[u]<smx1.first) smx1={mn[u], u};
}
dijkstra(node.second);
for (auto u:s)
{
if (u==node.first||u==node.second||mn[u]==inf) continue;
if (mn[u]<mx2.first) swap(mx2, smx2), mx2={mn[u], u};
else if (mn[u]<smx2.first) smx2={mn[u], u};
}
if (mx1.second!=smx1.second) ans=min(ans, mx1.first+mx2.first);
else ans=min({ans, mx1.first+smx2.first, smx1.first+mx2.first});
cout<<ans;
}
