#include <bits/stdc++.h>
using ll = long long;
const int nmax = 5e5 + 5;
const int mod = 1e9 + 7;
const int M = nmax * nmax + 5;
const ll oo = 1e18;
const int lg = 20;
#define fi first
#define se second
#define pii pair<ll, ll>
using namespace std;
int n, m, S, T, U, V;
priority_queue<pii, vector<pii>, greater<pii>> q;
ll dp[nmax][4], f[nmax], ans = oo;
pii a[nmax];
vector<pii> adj[nmax];
void build(int S, int x){
for(int i = 1; i <= n; ++i) dp[i][x] = oo;
dp[S][x] = 0;
q.push({0, S});
while(q.size()){
int u = q.top().se;
int lc = q.top().fi;
q.pop();
if(dp[u][x] != lc) continue;
for(auto [w, v] : adj[u]){
if(dp[v][x] > dp[u][x] + w){
dp[v][x] = dp[u][x] + w;
q.push({dp[v][x], v});
}
}
}
}
void sol(){
for(int i = 1; i <= n; ++i) a[i] = {dp[i][0], i};
sort(a + 1, a + 1 + n);
for(int i = 1; i <= n; ++i) f[i] = dp[i][2];
for(int i = n; i >= 1; --i){
int u = a[i].se;
for(auto [w, v] : adj[u]){
if(dp[u][0] + w == dp[v][0] && dp[v][0] + dp[v][3] == dp[T][0]){
f[u] = min(f[u], f[v]);
}
}
}
for(int i = 1; i <= n; ++i) ans = min(ans, f[i] + dp[i][1]);
for(int i = 1; i <= n; ++i) f[i] = dp[i][1];
for(int i = n; i >= 1; --i){
int u = a[i].se;
for(auto [w, v] : adj[u]){
if(dp[u][0] + w == dp[v][0] && dp[v][0] + dp[v][3] == dp[T][0]){
f[u] = min(f[u], f[v]);
}
}
}
for(int i = 1; i <= n; ++i) ans = min(ans, f[i] + dp[i][2]);
cout << ans;
}
int main(){
ios_base::sync_with_stdio(0);
cin.tie(0), cout.tie(0);
// freopen("code.inp", "r", stdin);
// freopen("code.out", "w", stdout);
cin >> n >> m >> S >> T >> U >> V;
for(int i = 1; i <= m; ++i){
int u, v, w;
cin >> u >> v >> w;
adj[u].push_back({w, v});
adj[v].push_back({w, u});
}
build(S, 0);
build(U, 1);
build(V, 2);
build(T, 3);
sol();
}
/*
*/
