#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pli = pair<ll, int>;
#define pb push_back
#define ff first
#define ss second
const ll inf = 1e18;
int main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int n, m, s, t, u, v; cin>>n>>m>>s>>t>>u>>v;
vector<pii> g[n + 1];
while (m--){
int x, y, w; cin>>x>>y>>w;
g[x].pb({y, w});
g[y].pb({x, w});
}
vector<int> P(n + 1);
auto f = [&](int x){
vector<ll> out(n + 1, inf);
vector<int> p(n + 1);
priority_queue<pli, vector<pli>, greater<pli>> pq;
out[x] = 0; pq.push({0, x});
while (!pq.empty()){
auto [d, y] = pq.top(); pq.pop();
for (auto [i, w]: g[y]){
ll dd = d + w;
if (dd < out[i]){
out[i] = dd;
pq.push({out[i], i});
p[i] = y;
}
}
}
if (x == s) P = p;
return out;
};
vector<ll> d[n + 1];
d[s] = f(s);
d[t] = f(t);
d[u] = f(u);
d[v] = f(v);
vector<int> G[n + 1];
for (int i = 1; i <= n; i++){
G[P[i]].pb(i);
}
vector<int> tin(n + 1), tout(n + 1);
int timer = 0;
function<void(int)> dfs = [&](int v){
tin[v] = ++timer;
for (int i: G[v]){
dfs(i);
}
tout[v] = timer;
};
dfs(s);
vector<int> a;
for (int i = 1; i <= n; i++){
if (d[s][t] == (d[s][i] + d[t][i])){
a.pb(i);
}
}
ll out = d[u][v];
for (int i: a){
for (int j: a){
if (tin[i] <= tin[j] && tout[i] >= tout[j]){
out = min(out, d[u][i] + d[v][j]);
out = min(out, d[v][i] + d[u][j]);
}
}
}
cout<<out<<"\n";
}
