#include<bits/stdc++.h>
using namespace std;
template<class T> bool minimize(T& a, T b){
if(a>b) return a=b, true;
return false;
}
template<class T> bool maximize(T& a, T b){
if(a<b) return a=b, true;
return false;
}
#define range(v) begin(v), end(v)
#define compact(v) v.erase(unique(range(v)), end(v))
typedef long long ll;
typedef unsigned long long ull;
const int N=1e5+5;
int n, m;
vector<pair<int, int>> g[N];
vector<int> par[N];
vector<ll> dijkstra(int st){
priority_queue<pair<ll, int>> pq;
vector<ll> d(n, -1); d[st]=0;
pq.push({0, st});
while(!pq.empty()){
ll cost; int u;
tie(cost, u)=pq.top(); pq.pop();
if(-cost!=d[u]) continue;
for(int i=0; i<g[u].size(); ++i){
int v, w; tie(v, w)=g[u][i];
if(d[v]==-1 or (d[v]>(d[u]+w))){
d[v]=d[u]+w;
pq.push({-d[v], v});
}
}
}
return d;
}
vector<ll> dijkstra_withTrace(int st){
vector<ll> d(n, -1); d[st]=0;
priority_queue<pair<ll, int>> pq;
pq.push({0, st});
while(!pq.empty()){
ll cost; int u;
tie(cost, u)=pq.top(); pq.pop();
if(-cost!=d[u]) continue;
for(int i=0; i<g[u].size(); ++i){
int v, w; tie(v, w)=g[u][i];
if(d[v]==-1 or (d[v]>d[u]+w)){
d[v]=d[u]+w;
par[v].clear(); par[v].push_back(u);
pq.push({-d[v], v});
}
else if(d[v]==d[u]+w) par[v].push_back(u);
}
}
return d;
}
void Zero_OP(){
int s, t, U, V; cin>>n>>m>>s>>t>>U>>V;
--s, --t, --U, --V;
while(m--){
int a, b, c; cin>>a>>b>>c;
--a, --b;
g[a].push_back({b, c});
g[b].push_back({a, c});
}
vector<ll> dU=dijkstra(U), dV=dijkstra(V), dS=dijkstra_withTrace(s);
ll ans=dU[V];
priority_queue<pair<ll, int>> pq;
vector<ll> d(n, -1); d[t]=dV[t];
pq.push({-d[t], t});
while(!pq.empty()){
ll cost; int u;
tie(cost, u)=pq.top(); pq.pop();
if(-cost!=d[u]) continue;
minimize(ans, d[u]+dU[u]);
for(int i=0; i<par[u].size(); ++i){
int v=par[u][i];
if(d[v]==-1 or (d[v]>min(d[u], dV[v]))){
d[v]=min(d[u], dV[v]);
pq.push({-d[v], v});
}
}
}
fill(range(d), -1); d[t]=dU[t];
pq.push({-d[t], t});
while(!pq.empty()){
ll cost; int u;
tie(cost, u)=pq.top(); pq.pop();
if(-cost!=d[u]) continue;
minimize(ans, d[u]+dV[u]);
for(int i=0; i<par[u].size(); ++i){
int v=par[u][i];
if(d[v]==-1 or (d[v]>min(d[u], dU[v]))){
d[v]=min(d[u], dU[v]);
pq.push({-d[v], v});
}
}
}
cout<<ans;
}
int main(){
ios_base::sync_with_stdio(0);
cin.tie(NULL); cout.tie(NULL);
Zero_OP();
return 0;
}
