#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ff first
#define ss second
const ll N = 1e5 + 7;
struct node{
queue<ll> from;
ll len = 1e18;
};
vector<vector<pair<ll,ll>>> a;
node b[N];
ll dis[N],fdis[N];
void dijsktra1(ll start)
{
set<pair<ll,pair<ll,ll>>> s;
s.insert({0,{start,start}});
while(!s.empty())
{
pair<ll,pair<ll,ll>> v = *s.begin();
s.erase(s.begin());
if(v.ff > b[v.ss.ff].len)continue;
dis[v.ss.ff] = max(dis[v.ss.ff],dis[v.ss.ss] + 1);
if(v.ff == b[v.ss.ff].len)
{
b[v.ss.ff].from.push(v.ss.ss);
continue;
}
b[v.ss.ff].len = v.ff;
b[v.ss.ff].from = queue<ll>();
b[v.ss.ff].from.push(v.ss.ss);
for(auto x : a[v.ss.ff])s.insert({b[v.ss.ff].len + x.ff,{x.ss,v.ss.ff}});
}
b[start].from.pop();
return;
}
void correct(ll start)
{
queue<ll> q;
q.push(start);
while(!q.empty())
{
ll v = q.front();
q.pop();
if(fdis[v] != -1)continue;
fdis[v] = dis[v];
while(!b[v].from.empty())
{
q.push(b[v].from.front());
b[v].from.pop();
}
}
return ;
}
ll st[N],dis2[N];
void dijsktra2(ll start)
{
set<pair<ll,pair<ll,ll>>> s;
s.insert({0,{start,-1}});
while(!s.empty())
{
pair<ll,pair<ll,ll>> v = *s.begin();
s.erase(s.begin());
if(v.ff > dis2[v.ss.ff])continue;
if(st[v.ss.ff] == 2)continue;
if(st[v.ss.ff] == 1 && v.ss.ss > -1)continue;
if(v.ss.ss == -1)st[v.ss.ff] = 2;
else st[v.ss.ff] = 1;
dis2[v.ss.ff] = v.ff;
for(auto x : a[v.ss.ff])
{
if(v.ss.ss == -1)
{
s.insert({dis2[v.ss.ff] + x.ff,{x.ss,-1}});
if(fdis[v.ss.ff] < fdis[x.ss] && fdis[x.ss] != -1 && fdis[v.ss.ff] != -1)s.insert({dis2[v.ss.ff],{x.ss,0}});
else if(fdis[v.ss.ff] != -1 && fdis[x.ss] != -1)s.insert({dis2[v.ss.ff],{x.ss,1}});
}
else if(v.ss.ss == 0)
{
if(fdis[v.ss.ff] < fdis[x.ss] && fdis[v.ss.ff] != -1 && fdis[x.ss] != -1)s.insert({dis2[v.ss.ff],{x.ss,0}});
s.insert({dis2[v.ss.ff] + x.ff,{x.ss,2}});
}
else if(v.ss.ss == 1)
{
if(fdis[v.ss.ff] > fdis[x.ss] && fdis[v.ss.ff] != -1 && fdis[x.ss] != -1)s.insert({dis2[v.ss.ff],{x.ss,1}});
else s.insert({dis2[v.ss.ff] + x.ff,{x.ss,2}});
}
else s.insert({dis2[v.ss.ff] + x.ff,{x.ss,2}});
}
}
return ;
}
int main()
{
ll n,m,s,t,u,v;
cin>>n>>m;
cin>>s>>t;
cin>>u>>v;
s--;t--;u--;v--;
a.resize(n);
for(ll i = 0;i < n;i++)fdis[i] = -1;
for(ll i = 0;i < n;i++)dis2[i] = 1e18;
for(ll i = 0;i < m;i++)
{
ll x,y,z;
cin>>x>>y>>z;x--;y--;
a[x].push_back({z,y});
a[y].push_back({z,x});
}
dijsktra1(s);
correct(t);
//cout<<b[t].len<<" ";
dijsktra2(u);
cout<<dis2[v]<<" ";
}
/*
6 7
2 4
2 4
1 2 1
1 6 2
2 6 3
2 5 1
2 3 4
3 4 2
6 4 3
*/
