#include<bits/stdc++.h>
using namespace std;
#define endl '\n'
using ll = long long;
using ld = long double;
#define pb push_back
#define sz size()
#define int long long
typedef pair<int, ll> pil;
const int maxn = 1e5 + 1;
const ll inf = 1e15;
vector<set<pil>> graph(maxn);
struct comp{
bool operator() (pil a, pil b){
return a.second > b.second;
}
};
struct edge {
int u, v; ll w;
// Ordenar las aristas por el menor peso
bool operator<(const edge& that) const {
return w < that.w; // Cambiar '<' por '>' para hallar el Maximal Spanning Tree
}
};
// Complejidad O(m*log(n))
void dijkstra(int source, int n, vector<ll>& d){
for(int i = 1; i <= n; i++) d[i] = inf;
d[source] = 0;
priority_queue<pil, vector<pil>, comp> pq;
pq.push({source, 0});
while(!pq.empty()){
int u = pq.top().first; ll w1 = pq.top().second;
pq.pop();
if(d[u] < w1) continue;
for(pil edge : graph[u]){
int v = edge.first; ll w2 = edge.second;
if(d[v] > w1 + w2){
d[v] = w1 + w2;
pq.push({v, d[v]});
}
}
}
}
void change(int s, int t, vector<ll>& ds, vector<ll>& dt, vector<edge>& edges){
for(edge e : edges){
int u = e.u, v = e.v; ll w = e.w;
if(ds[u] + w + dt[v] == ds[t]){
graph[u].erase({v, w});
graph[u].insert({v, 0});
}
else if(ds[v] + w + dt[u] == ds[t]){
graph[v].erase({u, w});
graph[v].insert({u, 0});
}
}
}
signed solver(){
int n, m, s, t, u, v; cin>>n>>m>>s>>t>>u>>v;
vector<edge> edges;
for(int i = 0; i < m; i++){
int a, b; ll w;
cin>>a>>b>>w;
edges.pb({a, b, w});
graph[a].insert({b, w});
graph[b].insert({a, w});
}
vector<ll> ds(n+1), dt(n+1), du(n+1), dv(n+1);
dijkstra(s, n, ds);
dijkstra(t, n, dt);
change(s, t, ds, dt, edges);
dijkstra(u, n, du);
dijkstra(v, n, dv);
cout<<min(du[v], dv[u])<<endl;
}
int main(){
ios_base::sync_with_stdio(0);cin.tie(NULL);
int t = 1;
// cin>>t;
while(t--){
solver();
}
return 0;
}
