#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define f first
#define s second
#define pii pair<int32_t,int32_t>
#define ppii pair<int,pii>
#define vi vector<int>
#define pb push_back
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define F(n) for(int i=0;i<n;i++)
#define lb lower_bound
#define ub upper_bound
#define fastio ios::sync_with_stdio(false);cin.tie(NULL);
#pragma GCC optimize ("03,unroll-lopps")
#define sz(x) (int)((x).size())
#define int long long
using namespace std;
const int mod=1e9+7,mxn=2e5,inf=1e9,minf=-1e9,lg=30,Mxn=1e9;
//#undef int
int n,k,m,d,q;
void setIO(string name){
ios_base::sync_with_stdio(0); cin.tie(0);
freopen((name+".in").c_str(),"r",stdin);
freopen((name+".out").c_str(),"w",stdout);
}
vector<pii>dist[mxn+10];
vector<pii>adj[mxn+10];
int have(int x,pii a){
for(auto i:dist[x])if(i==a)return 1;
return 0;
}
bool put(int x,pii a){
for(auto &i:dist[x])if(i.s==a.s){
if(i.f>a.f)return i.f=a.f,1;
return 0;
}
if(dist[x].size()<3)return dist[x].pb(a),1;
sort(all(dist[x]));
if(a.f<dist[x].back().f){
dist[x].pop_back();
dist[x].pb(a);
return 1;
}
return 0;
}
bool good(pii a,pii b){
if(a.f==b.f||a.f==b.s||a.s==b.f||a.s==b.s)return 0;
return 1;
}
struct seg{
int v[mxn+10];
vector<int>keep;
void init(){
keep.clear();
for(int i=0;i<=2*n;i++)v[i]=inf;
}
void update(int pos,int val){
pos+=n;
keep.pb(pos);
v[pos]=min(v[pos],val);
for(int i=pos;i>0;i>>=1)v[i>>1]=min(v[i],v[i^1]);
}
int qry(int l,int r){
int ans=inf;
for(l+=n,r+=n;l<=r;l>>=1,r>>=1){
if(l&1)ans=min(ans,v[l++]);
if(!(r&1))ans=min(ans,v[r--]);
}
return ans;
}
void re(){
for(auto pos:keep){
v[pos]=inf;
for(int i=pos;i>0;i>>=1)v[i>>1]=min(v[i],v[i^1]);
}
keep.clear();
}
}t;
int ans=inf;
vector<pii>event[mxn+10];
struct rec{
int LX,RX,LY,RY,val;
};
bool cmpF(rec a,rec b){
return a.LY>b.LY;
}
bool cmpS(rec a,rec b){
return a.RY<b.RY;
}
void dnc(int l,int r,vector<rec>Q){
int mid=l+(r-l)/2;
vector<rec>L,R;
sort(all(Q),cmpF);
int cur=mid;
for(auto i:Q){
if(i.LY<=mid&&i.RY>mid){
while(i.LY<=cur){
for(auto j:event[cur])t.update(j.f,j.s);
cur--;
}
ans=min(ans,i.val+t.qry(i.LX,i.RX));
}
else if(i.RY<=mid)L.pb(i);
else R.pb(i);
}
t.re();
sort(all(Q),cmpS);
cur=mid+1;
for(auto i:Q){
if(i.LY<=mid&&i.RY>mid){
while(i.RY>=cur){
for(auto j:event[cur])t.update(j.f,j.s);
cur++;
}
ans=min(ans,i.val+t.qry(i.LX,i.RX));
}
}
t.re();
if(l==r)return;
dnc(l,mid,L);
dnc(mid+1,r,R);
}
bool cmp(pair<int,pii> a,pair<int,pii> b){return a.s.s<b.s.s;}
int32_t main(){
fastio
cin>>n>>m>>k;
for(int i=0;i<m;i++){
int a,b,c;cin>>a>>b>>c;
adj[a].pb({b,c});
adj[b].pb({a,c});
}
vector<int>SP(k);
priority_queue<pair<int,pii>,vector<pair<int,pii>>,greater<pair<int,pii>>>pq;
for(auto &i:SP){
cin>>i;
pq.push({0,{i,i}});
}
while(!pq.empty()){
int C=pq.top().f,cur=pq.top().s.f,F=pq.top().s.s;
pq.pop();
if(cur!=F&&!have(cur,{C,F}))continue;
for(auto i:adj[cur]){
if(i.f!=F&&put(i.f,{C+i.s,F}))pq.push({C+i.s,{i.f,F}});
}
}
vector<pair<int,pii>>have;
for(auto i:SP){
for(auto j:dist[i])have.pb({j.f,{i,j.s}});
}
for(auto &i:have)if(i.s.f>i.s.s)swap(i.s.f,i.s.s);
int cur=0;
sort(all(have),cmp);
t.init();
for(int i=0;i<have.size();i++){
vector<pii>upd;
while(cur<have.size()&&have[cur].s.s==have[i].s.s){
ans=min(ans,have[cur].f+t.qry(1,have[cur].s.f-1));
ans=min(ans,have[cur].f+t.qry(have[cur].s.f+1,have[cur].s.s-1));
ans=min(ans,have[cur].f+t.qry(have[cur].s.s+1,n));
upd.pb({have[cur].s.f,have[cur].f});
cur++;
}
for(auto i:upd)t.update(i.f,i.s);
}
cur=0;
reverse(all(have));
t.init();
for(int i=0;i<have.size();i++){
vector<pii>upd;
while(cur<have.size()&&have[cur].s.s==have[i].s.s){
ans=min(ans,have[cur].f+t.qry(1,have[cur].s.f-1));
ans=min(ans,have[cur].f+t.qry(have[cur].s.f+1,have[cur].s.s-1));
ans=min(ans,have[cur].f+t.qry(have[cur].s.s+1,n));
upd.pb({have[cur].s.f,have[cur].f});
cur++;
}
for(auto i:upd)t.update(i.f,i.s);
}
t.init();
vector<rec>ask;
for(auto i:have){
ask.pb((rec){1,i.s.f-1,i.s.s+1,i.s.f-1,i.f});
ask.pb((rec){i.s.f+1,i.s.s-1,i.s.s+1,i.s.f-1,i.f});
ask.pb((rec){i.s.s+1,n,i.s.s+1,i.s.f-1,i.f});
}
dnc(1,n,ask);
cout<<ans;
}
/*
*/
Compilation message (stderr)
RelayMarathon.cpp:16:40: warning: bad option '-funroll-lopps' to pragma 'optimize' [-Wpragmas]
16 | #pragma GCC optimize ("03,unroll-lopps")
| ^
RelayMarathon.cpp:23:23: warning: bad option '-funroll-lopps' to attribute 'optimize' [-Wattributes]
23 | void setIO(string name){
| ^
RelayMarathon.cpp:30:21: warning: bad option '-funroll-lopps' to attribute 'optimize' [-Wattributes]
30 | int have(int x,pii a){
| ^
RelayMarathon.cpp:34:21: warning: bad option '-funroll-lopps' to attribute 'optimize' [-Wattributes]
34 | bool put(int x,pii a){
| ^
RelayMarathon.cpp:48:22: warning: bad option '-funroll-lopps' to attribute 'optimize' [-Wattributes]
48 | bool good(pii a,pii b){
| ^
RelayMarathon.cpp:55:19: warning: bad option '-funroll-lopps' to attribute 'optimize' [-Wattributes]
55 | void init(){
| ^
RelayMarathon.cpp:60:36: warning: bad option '-funroll-lopps' to attribute 'optimize' [-Wattributes]
60 | void update(int pos,int val){
| ^
RelayMarathon.cpp:66:28: warning: bad option '-funroll-lopps' to attribute 'optimize' [-Wattributes]
66 | int qry(int l,int r){
| ^
RelayMarathon.cpp:74:17: warning: bad option '-funroll-lopps' to attribute 'optimize' [-Wattributes]
74 | void re(){
| ^
RelayMarathon.cpp:87:22: warning: bad option '-funroll-lopps' to attribute 'optimize' [-Wattributes]
87 | bool cmpF(rec a,rec b){
| ^
RelayMarathon.cpp:90:22: warning: bad option '-funroll-lopps' to attribute 'optimize' [-Wattributes]
90 | bool cmpS(rec a,rec b){
| ^
RelayMarathon.cpp:93:34: warning: bad option '-funroll-lopps' to attribute 'optimize' [-Wattributes]
93 | void dnc(int l,int r,vector<rec>Q){
| ^
RelayMarathon.cpp:128:41: warning: bad option '-funroll-lopps' to attribute 'optimize' [-Wattributes]
128 | bool cmp(pair<int,pii> a,pair<int,pii> b){return a.s.s<b.s.s;}
| ^
RelayMarathon.cpp:129:14: warning: bad option '-funroll-lopps' to attribute 'optimize' [-Wattributes]
129 | int32_t main(){
| ^
RelayMarathon.cpp: In function 'void setIO(std::string)':
RelayMarathon.cpp:25:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
25 | freopen((name+".in").c_str(),"r",stdin);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
RelayMarathon.cpp:26:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
26 | freopen((name+".out").c_str(),"w",stdout);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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