#include <bits/stdc++.h>
#define maxn 100005
#define pii pair<int,int>
#define INF 100000000000000000
using namespace std;
int n,m;
vector<pii>adj[maxn];
int s,t;
long long ds[maxn];
long long dt[maxn];
long long duu[maxn];
int u,v;
long long du[maxn][3];
int first[maxn];
//0 nije poceo
//1 traje
//2 prosao
vector<int>mv[3];
priority_queue<pair<long long,int>>pq;
priority_queue<pair<long long,pii>>pq2;
long long manji(long long aa,long long bb)
{
if(aa<bb)return aa;
return bb;
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
mv[0].push_back(0);
mv[0].push_back(1);
mv[1].push_back(1);
mv[1].push_back(2);
mv[2].push_back(2);
cin>>n>>m;
cin>>s>>t;
cin>>u>>v;
for(int i=0;i<m;i++)
{
int x,y,c;
cin>>x>>y>>c;
adj[x].push_back({y,c});
adj[y].push_back({x,c});
}
//cout<<endl;
for(int i=1;i<=n;i++)ds[i]=INF;
pq.push({0LL,s});
ds[s]=0LL;
while(!pq.empty())
{
int x=pq.top().second;
pq.pop();
for(auto zz:adj[x])
{
int y=zz.first;
int ras=zz.second;
if(ds[y]>ds[x]+ras)
{
ds[y]=ds[x]+ras;
pq.push({-ds[y],y});
}
}
}
//for(int i=1;i<=n;i++)cout<<i<<" "<<ds[i]<<endl;cout<<endl;
for(int i=1;i<=n;i++)dt[i]=INF;
pq.push({0LL,t});
dt[t]=0LL;
while(!pq.empty())
{
int x=pq.top().second;
pq.pop();
for(auto zz:adj[x])
{
int y=zz.first;
int ras=zz.second;
if(dt[y]>dt[x]+ras)
{
dt[y]=dt[x]+ras;
pq.push({-dt[y],y});
}
}
}
//for(int i=1;i<=n;i++)cout<<i<<" "<<dt[i]<<endl;cout<<endl;
for(int i=1;i<=n;i++)duu[i]=INF;
pq.push({0LL,u});
duu[u]=0LL;
while(!pq.empty())
{
int x=pq.top().second;
pq.pop();
for(auto zz:adj[x])
{
int y=zz.first;
int ras=zz.second;
if(duu[y]>duu[x]+ras)
{
duu[y]=duu[x]+ras;
pq.push({-duu[y],y});
}
}
}
//for(int i=1;i<=n;i++)cout<<i<<" "<<duu[i]<<endl;cout<<endl;
for(int i=1;i<=n;i++)du[i][0]=du[i][1]=du[i][2]=INF;
pq2.push({0LL,{u,0}});
pq2.push({0LL,{u,2}});
du[u][0]=0LL;
du[u][2]=0LL;
du[u][1]=0LL;
first[u]=u;
if(ds[u]+dt[u]!=ds[t])du[u][1]=INF;
pq2.push({-du[u][1],{u,1}});
while(!pq2.empty())
{
int x=pq2.top().second.first;
int ty=pq2.top().second.second;
pq2.pop();
for(auto zz:adj[x])
{
int y=zz.first;
for(auto tt:mv[ty])
{
int ras=zz.second;
int prvi=first[x];
if(ty!=1)prvi=x;
if(tt==1)
{
//if(x==2 && ty==0 && y==1 && tt==1)cout<<"qrac1 "<<y<<" "<<prvi<<" "<<ds[prvi]<<" "<<dt[y]<<" "<<duu[x]<<" "<<duu[prvi]<<" "<<ras<<" "<<ds[t]<<endl;
long long resss=manji(ds[prvi]+dt[y],dt[prvi]+ds[y]);
if(resss+duu[x]-duu[prvi]+ras!=ds[t])continue;
//if(x==2 && ty==0 && y==1 && tt==1)cout<<"qrac2"<<endl;
ras=0;
}
if(du[y][tt]>du[x][ty]+ras)
{
du[y][tt]=du[x][ty]+ras;
pq2.push({-du[y][tt],{y,tt}});
if(tt==1)first[y]=prvi;
}
}
}
}
//for(int i=1;i<=n;i++)cout<<i<<" "<<du[i][0]<<" "<<du[i][1]<<" "<<du[i][2]<<endl;
long long sol=du[v][0];
if(sol>du[v][1])sol=du[v][1];
if(sol>du[v][2])sol=du[v][2];
cout<<sol<<endl;
return 0;
}
