#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][3];//directie drum pentru 1/astfel 1 egal crescator 2 descrescator 0 bag pula;
struct drum
{
int unde,cost;
};
struct coada
{
int nod;
long long cost;
int a_folosit;//asta e de 3 tipuri
int drumulet;
};
struct compara
{
bool operator()(coada &x,coada &y)
{
return x.cost>y.cost;
}
};
void reset()
{
for(int i=1; i<=n; i++)
{
for(int j=0; j<2; j++)
for(int k=0; k<3; k++)
dp[i][j][k]=infinit;
}
}
vector<drum>adj[N];
void cauta_drum(int start)
{
for(int i=1; i<=n; i++)
costuri[i]=infinit;
priority_queue<coada,vector<coada>,compara>pq;
reset();
costuri[start]=0;
coada x= {start,0,0,0};
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();
for(auto u:adj[nod])
{
if(costuri[u.unde]+u.cost==costuri[nod])
{
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]=0;
pq.push({start,0,0,0});
while(!pq.empty())
{
int nod,tip;
long long cost;
nod=pq.top().nod;
cost=pq.top().cost;
tip=pq.top().a_folosit;
int drum=pq.top().drumulet;
pq.pop();
for(auto u:adj[nod])
{
long long end=cost+u.cost;
if(tip>0)
{
if(dp[u.unde][1][0]>end)
{
dp[u.unde][1][0]=end;
pq.push({u.unde,end,2,0});
}
}
else
{
if(dp[u.unde][0][0]>end)
{
dp[u.unde][0][0]=end;
pq.push({u.unde,end,0,0});
}
}
}
if(tip<2)
{
for(auto u:pereche[nod])
{
if(drum==0)
{
if(costuri[nod]<costuri[u])
{
if(dp[u][1][1]>dp[nod][tip][0])
{
dp[u][1][1]=dp[nod][tip][0];
pq.push({u,dp[u][1][1],1,1});
}
}
else
{
if(dp[u][1][2]>dp[nod][tip][0])
{
dp[u][1][2]=dp[nod][tip][0];
pq.push({u,dp[u][1][2],1,2});
}
}
}
else
{
if(drum==1)
{
if(costuri[nod]<costuri[u])
{
if(dp[u][1][1]>dp[nod][1][1])
{
dp[u][1][1]=dp[nod][1][1];
pq.push({u,dp[u][1][1],1,1});
}
}
}
else if(costuri[nod]>costuri[u])
{
if(dp[u][1][2]>dp[nod][1][2])
{
dp[u][1][2]=dp[nod][1][2];
pq.push({u,dp[u][1][2],1,2});
}
}
}
}
}
}
}
int main()
{
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
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);
long long ans=infinit;
for(int i=0; i<2; i++)
{
for(int k=0; k<=2; k++)
ans=min(ans,dp[mag1][i][k]);
}
cout<<ans<<'\n';
return 0;
}
