#include <bits/stdc++.h>
using namespace std;
const int N=1e5+1;
const long long infinit=1e18;
int n,m,casa,scoala,mag1,mag2;
long long costuri[N];
vector<int>pereche[N];
long long dp[N][2];
struct drum
{
int unde,cost;
};
struct coada
{
int nod;
long long cost;
int a_folosit;//asta e de 3 tipuri
};
struct compara
{
bool operator()(coada &x,coada &y)
{
return x.cost<y.cost;
}
};
void reset()
{
for(int i=1;i<=n;i++)
{costuri[i]=infinit;
dp[i][0]=infinit;
dp[i][1]=infinit;}
}
vector<drum>adj[N];
void cauta_drum(int start)
{
priority_queue<coada,vector<coada>,compara>pq;
reset();
costuri[start]=0;
coada x={start,0,0};
pq.push(x);
while(!pq.empty())
{
coada actual=pq.top();
pq.pop();
for(auto u:adj[actual.nod])
{
if(costuri[u.unde]>actual.cost+u.cost)
{
costuri[u.unde]=actual.cost+u.cost;
pq.push({u.unde,costuri[u.unde],0});
}
}
}
}
void back_drum(int start)
{
queue<int>cod;
cod.push(start);
vector<bool>viz(n+1,0);
viz[start]=true;
while(!cod.empty())
{
int nod=cod.front();
cod.pop();
long long mn=costuri[nod];
for(auto u:adj[nod])
{
mn=min(mn,costuri[u.unde]);
}
if(mn==costuri[nod])
continue;
for(auto u:adj[nod])
{
if(costuri[u.unde]==mn)
{
pereche[u.unde].push_back(nod);
pereche[nod].push_back(u.unde);
if(!viz[u.unde])
{
viz[u.unde]=true;
cod.push(u.unde);
}
}
}
}
}
void calculeaza_cost(int start)
{
reset();
priority_queue<coada,vector<coada>,compara>pq;
dp[start][0]=0;
pq.push({start,0,0});
while(!pq.empty())
{
int nod,tip;
long long cost;
nod=pq.top().nod;
cost=pq.top().cost;
tip=pq.top().a_folosit;
pq.pop();
for(auto u:adj[nod])
{
long long end=cost+u.cost;
if(tip>0)
{
if(dp[u.unde][1]>end)
{
dp[u.unde][1]=end;
pq.push({u.unde,end,2});
}
}
else
{
if(dp[u.unde][0]>end)
{
dp[u.unde][0]=end;
pq.push({u.unde,end,0});
}
}
}
if(tip<2)
{
for(auto u:pereche[nod])
{
if(dp[u][1]>dp[nod][tip])
{
dp[u][1]=dp[nod][tip];
pq.push({u,dp[u][1],1});
}
}
}
}
}
int main()
{
cin>>n>>m;
cin>>casa>>scoala;
cin>>mag1>>mag2;
for(int i=1;i<=m;i++)
{
int nod1,nod2,cost;
cin>>nod1>>nod2>>cost;
adj[nod1].push_back({nod2,cost});
adj[nod2].push_back({nod1,cost});
}
cauta_drum(casa);
back_drum(scoala);
calculeaza_cost(mag2);
cout<<min(dp[mag1][0],dp[mag1][1])<<'\n';
return 0;
}
