#include <cstdio>
#include <stdio.h>
#include <stdbool.h>
#include <iostream>
#include <map>
#include <vector>
#include <climits>
#include <stack>
#include <string>
#include <queue>
#include <algorithm>
#include <set>
#include <unordered_set>
#include <unordered_map>
#include <cmath>
#include <cctype>
#include <bitset>
#include <iomanip>
#include <cstring>
#include <numeric>
#include <cassert>
using namespace std;
#define int long long
#define pii pair<int, int>
#define mp make_pair
#define pb push_back
#define fi first
#define se second
int n;
vector<int> du, dv;
vector<vector<pii> > graph;
vector<int> dijk(int s){
vector<int> dj(n+1, LLONG_MAX/2);
priority_queue<pii, vector<pii>, greater<pii> > pq;
dj[s]=0;
pq.push(mp(0, s));
while (pq.size()){
int d=pq.top().fi, node=pq.top().se;
pq.pop();
if (d!=dj[node])continue;
for (auto num:graph[node])if (dj[node]+num.se<dj[num.fi]){
dj[num.fi]=dj[node]+num.se;
pq.push(mp(dj[num.fi], num.fi));
}
}
return dj;
}
int dijk2(int s, int t){
vector<int> dj(n+1, LLONG_MAX/2), u(n+1, LLONG_MAX/2), v(n+1, LLONG_MAX/2);
vector<bool> visited(n+1, 0);
priority_queue<pair<int, pii>, vector<pair<int, pii> >, greater<pair<int, pii> > > pq;
pq.push(mp(0, mp(s, 0)));
while (pq.size()){
int d=pq.top().fi, node=pq.top().se.fi, par=pq.top().se.se;
pq.pop();
if (!visited[node]){
visited[node]=1;
dj[node]=d;
u[node]=min(u[par], du[node]);
v[node]=min(v[par], dv[node]);
for (auto num:graph[node])pq.push(mp(d+num.se, mp(num.fi, node)));
}
else if (d==dj[node]&&min(u[par], du[node])+min(v[par], dv[node])<u[node]+v[node]){
u[node]=min(u[par], du[node]);
v[node]=min(v[par], dv[node]);
}
}
return u[t]+v[t];
}
int32_t main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int m, s, t, u, v, a, b, c;
cin>>n>>m>>s>>t>>u>>v;
graph.resize(n+1);
while (m--){
cin>>a>>b>>c;
graph[a].pb(mp(b, c));
graph[b].pb(mp(a, c));
}
du=dijk(u), dv=dijk(v);
cout<<min(du[v], dijk2(s, t));
}
