#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <set>
#include <map>
#include <algorithm>
#include <time.h>
#include <algorithm>
#include <queue>
#include <utility>
#include <map>
using namespace std;
vector < pair < long long , pair < long long , long long > > > Next[200005];
vector < long long > Next2[200005];
priority_queue < pair < long long , long long > , vector < pair < long long , long long > > , greater < pair < long long , long long > > > dij;
queue < long long > ttt;
bool use[200005]={0};
bool have[200005]={0};
long long small[100005]={0};
int main()
{
long long N,M,S,T,U,V,a,b,c,i,ans=1e18;
scanf("%lld %lld",&N,&M);
scanf("%lld %lld %lld %lld",&S,&T,&U,&V);
for(i=1;i<=N;i++) small[i]=-1;
for(i=0;i<M;i++)
{
scanf("%lld %lld %lld",&a,&b,&c);
Next[a].push_back(make_pair(i,make_pair(b,c)));
Next[b].push_back(make_pair(i,make_pair(a,c)));
}
dij.push(make_pair(0,S));
while(!dij.empty())
{
a=dij.top().first;
b=dij.top().second;
dij.pop();
if(small[b]!=-1) continue;
small[b]=a;
for(auto i:Next[b]) dij.push(make_pair(a+i.second.second,i.second.first));
}
ttt.push(T);
while(!ttt.empty())
{
i=ttt.front();
ttt.pop();
if(have[i]) continue;
have[i]=1;
for(auto j:Next[i])
{
if(small[i]-j.second.second==small[j.second.first])
{
use[j.first]=1;
ttt.push(j.second.first);
Next2[j.second.first].push_back(i);
}
}
}
for(i=1;i<=N;i++) small[i]=-1;
dij.push(make_pair(0,U));
while(!dij.empty())
{
a=dij.top().first;
b=dij.top().second;
dij.pop();
if(small[b]!=-1) continue;
small[b]=a;
for(auto i:Next[b]) dij.push(make_pair(a+i.second.second,i.second.first));
for(auto i:Next2[b]) dij.push(make_pair(a,i));
}
ans=min(ans,small[V]);
for(i=1;i<=N;i++) small[i]=-1;
dij.push(make_pair(0,V));
while(!dij.empty())
{
a=dij.top().first;
b=dij.top().second;
dij.pop();
if(small[b]!=-1) continue;
small[b]=a;
for(auto i:Next[b]) dij.push(make_pair(a+i.second.second,i.second.first));
for(auto i:Next2[b]) dij.push(make_pair(a,i));
}
ans=min(ans,small[U]);
printf("%lld\n",ans);
return 0;
}
