#include <stdio.h>
#include <stdlib.h>
#include <algorithm>
#include <iostream>
#include <cstring>
#include <vector>
#include <queue>
#include <string>
#include <bitset>
#include <set>
#include <fstream>
#define ll long long
#include <bits/stdc++.h>
using namespace std;
const ll INF=LLONG_MAX/2;
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
//cout.tie(0);
//freopen("shortcut.in", "r", stdin);
//freopen("shortcut.out", "w", stdout);
ll n,m;
cin>>n>>m;
ll s,t;
cin>>s>>t;
ll u,v;
cin>>u>>v;
vector<pair<int,int> > adj[n+1];
for(int i=0; i<m; i++)
{
ll a,b,c;
cin>>a>>b>>c;
adj[a].push_back(make_pair(c, b));
adj[b].push_back(make_pair(c,a));
}
vector<ll> du(n+1,INF),dv(n+1, INF),ds(n+1, INF),dt(n+1, INF);
priority_queue<pair<ll,ll>, vector<pair<ll,ll> >, greater<pair<ll,ll> > > pq;
du[u]=0;
pq.push(make_pair(0,u));
while(!pq.empty())
{
ll cur=pq.top().second;
ll c=pq.top().first;
pq.pop();
if(du[cur]!=c) continue;
for(auto to : adj[cur])
{
ll ver=to.second;
ll w=to.first;
if(du[cur]+w<du[ver])
{
du[ver]=du[cur]+w;
pq.push(make_pair(du[ver],ver));
}
}
}
dv[v]=0;
pq.push(make_pair(0,v));
while(!pq.empty())
{
ll cur=pq.top().second;
ll c=pq.top().first;
pq.pop();
if(dv[cur]!=c) continue;
for(auto to : adj[cur])
{
ll ver=to.second;
ll w=to.first;
if(dv[cur]+w<dv[ver])
{
dv[ver]=dv[cur]+w;
pq.push(make_pair(dv[ver],ver));
}
}
}
vector<ll> dpU(n+1,INF);
vector<ll> dpV(n+1,INF);
ds[s]=0;
pq.push(make_pair(0,s));
while(!pq.empty())
{
ll cur=pq.top().second;
ll c=pq.top().first;
pq.pop();
if(ds[cur]!=c)
{
continue;
}
for(auto to: adj[cur])
{
ll ver=to.second;
ll w=to.first;
if(ds[cur]+w<ds[ver])
{
ds[ver]=ds[cur]+w;
pq.push(make_pair(ds[ver],ver));
dpU[ver]=min(du[ver], dpU[cur]);
dpV[ver]=min(dv[ver], dpV[cur]);
}
else if(ds[cur]+w==ds[ver])
{
if(min(du[ver], dpU[cur])+min(dv[ver], dpV[cur])<=dpU[ver]+dpV[ver])
{
dpU[ver]=min(du[ver], dpU[cur]);
dpV[ver]=min(dv[ver], dpV[cur]);
}
}
}
}
ll ans=du[v];
ans=min(ans, dpU[t]+dpV[t]);
dpU.resize(n+1,INF);
dpV.resize(n+1,INF);
dt[t]=0;
pq.push(make_pair(0,t));
while(!pq.empty())
{
ll cur=pq.top().second;
ll c=pq.top().first;
if(dt[cur]!=c)
{
continue;
}
for(auto to: adj[cur])
{
ll ver=to.second;
ll w=to.first;
if(dt[cur]+w<dt[ver])
{
dt[ver]=dt[cur]+w;
pq.push(make_pair(dt[ver],ver));
dpU[ver]=min(du[ver], dpU[cur]);
dpV[ver]=min(dv[ver], dpV[cur]);
}
else if(dt[cur]+w==dt[ver])
{
if(min(du[ver], dpU[cur])+min(dv[ver], dpV[cur])<=dpU[ver]+dpV[ver])
{
dpU[ver]=min(du[ver], dpU[cur]);
dpV[ver]=min(dv[ver], dpV[cur]);
}
}
}
}
ll ans2=dv[u];
ans2=min(ans2, dpU[s]+dpV[s]);
ll ansfinal=min(ans, ans2);
cout<<ansfinal<<endl;
return 0;
}
