This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define int long long
#define fi first
#define se second
const int N=1e5+50;
const int inf=1e15;
vector<pair<int,int> >E[N];
map<pair<int,int>,int>edges;
signed main()
{
int n,m;cin>>n>>m;
int A,B;cin>>A>>B;
int U,V;cin>>U>>V;
/*int edges[n+1][n+1];
for(int i=1;i<=n;i++) for(int j=1;j<=n;j++) edges[i][j]=inf;
int dp[n+1][n+1];
for(int i=1;i<=n;i++) for(int j=1;j<=n;j++) dp[i][j]=inf;*/
for(int i=1;i<=m;i++)
{
int u,v,w;cin>>u>>v>>w;
E[u].pb({v,w});
E[v].pb({u,w});
edges[{u,v}]=edges[{v,u}]=w;
/*edges[u][v]=w;
edges[v][u]=w;
dp[u][v]=dp[v][u]=w;*/
}
/*for(int j=1;j<=n;j++)
{
int dist[n+1];
bool was[n+1]={0};
priority_queue<pair<int,int> >pq;
for(int i=1;i<=n;i++) dist[i]=inf;
dist[j]=0;
pq.push({0,j});
while(!pq.empty())
{
pair<int,int> x=pq.top();
pq.pop();
if(was[x.se]) continue;
was[x.se]=true;
for(auto i:E[x.se])
{
if(!was[i.fi])
{
dist[i.fi]=min(dist[i.fi],-x.fi+i.se);
pq.push({-dist[i.fi],i.fi});
}
}
}
for(int i=1;i<=n;i++)
{
dp[j][i]=dist[i];
}
}*/
int dist[n+1];
bool was[n+1]={0};
priority_queue<pair<int,int> >pq;
for(int i=1;i<=n;i++) dist[i]=inf;
dist[A]=0;
pq.push({0,A});
int parent[n+1];
while(!pq.empty())
{
pair<int,int> x=pq.top();
pq.pop();
if(was[x.se]) continue;
was[x.se]=true;
for(auto i:E[x.se])
{
if(!was[i.fi])
{
dist[i.fi]=min(dist[i.fi],-x.fi+i.se);
pq.push({-dist[i.fi],i.fi});
parent[i.fi]=x.se;
}
}
}
int C=B;
while(C!=A)
{
//cout<<C<<" ";
int x=parent[C];
edges[{x,C}]=edges[{C,x}]=0;
C=x;
}
//cout<<endl;
//for(int i=1;i<=n;i++) for(int j=1;j<=n;j++) cout<<i<<" "<<j<<": "<<edges[{i,j}]<<" "<<edges[{j,i}]<<endl;
for(int i=1;i<=n;i++)was[i]=false;
for(int i=1;i<=n;i++) dist[i]=inf;
while(!pq.empty()) pq.pop();
dist[U]=0;
pq.push({0,U});
while(!pq.empty())
{
pair<int,int> x=pq.top();
pq.pop();
if(was[x.se]) continue;
was[x.se]=true;
for(auto i:E[x.se])
{
if(!was[i.fi])
{
dist[i.fi]=min(dist[i.fi],-x.fi+edges[{i.fi,x.se}]);
pq.push({-dist[i.fi],i.fi});
}
}
}
//for(int i=1;i<=n;i++) cout<<dist[i]<<" ";
//cout<<endl;
int res=dist[V];
/*int dp1[n+1][n+1];
for(int i=1;i<=n;i++) for(int j=1;j<=n;j++) dp1[i][j]=inf;
for(int i=1;i<=n;i++) edges[i][i]=0;
for(int i=1;i<=n;i++)
{
dp1[i][i]=0;
for(int j=1;j<=i;j++)
{
for(int k=1;k<i;k++)
{
dp1[i][j]=min(dp1[i][j],edges[i][k]+dp1[k][j]);
}
dp1[j][i]=dp1[i][j];
}
for(int j=1;j<i;j++)
{
for(int k=1;k<i;k++)
{
dp1[j][k]=min(dp1[j][k],min(edges[k][i]+dp1[i][j],edges[j][i]+dp1[i][k]));
}
}
}
for(int i=1;i<=n;i++) for(int j=1;j<=n;j++) if(dp[i][j]!=dp1[i][j]) cout<<i<<" "<<j<<": "<<dp[i][j]<<" "<<dp1[i][j]<<endl;*/
/*int res=dp[U][V];
for(int i=1;i<=n;i++)
{
for(int j=1;j<=n;j++)
{
if(dp[A][i]+dp[i][j]+dp[j][B]==dp[A][B]) res=min(res,min(dp[U][i]+dp[j][V],dp[V][i]+dp[U][j]));
}
}*/
//res=dp[U][V]-res;
cout<<res<<endl;
return 0;
}
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