#include <bits/stdc++.h>
using namespace std;
#define int long long
#define all(x) x.begin(), x.end()
#define pb push_back
#define ar array
#define nl '\n'
template <typename A, typename B>
bool chmin(A &a, const B &b) {
if(a > b) {
return a = b, true;
}
return false;
}
template <typename A, typename B>
bool chmax(A &a, const B &b) {
if(a < b) {
return a = b, true;
}
return false;
}
const int inf = 1e18;
void solve() {
int n, m; cin >> n >> m;
int S, T, U, V; cin >> S >> T >> U >> V;
S--, T--, U--, V--;
vector<vector<ar<int, 2>>> adj(n);
for(int i = 0; i < m; i++) {
int u, v, w; cin >> u >> v >> w;
u--, v--;
adj[u].pb({v, w});
adj[v].pb({u, w});
}
auto D = [&](int s, vector<int> &d) -> void {
fill(all(d), inf);
d[s] = 0;
priority_queue<ar<int, 2>, vector<ar<int, 2>>, greater<>> pq;
pq.push({0, s});
while(!pq.empty()) {
auto [d_v, v] = pq.top();
pq.pop();
if(d_v != d[v]) continue;
for(auto [to, w] : adj[v]) {
if( chmin(d[to], d[v] + w) ) {
pq.push({d[to], to});
}
}
}
};
vector<int> du(n), dv(n), ds(n);
D(U, du), D(V, dv);
vector<vector<int>> dp(2, vector<int>(n, inf));
int ans = du[V];
auto D2 = [&](int s, int t) -> void {
fill(all(dp[0]), inf);
fill(all(dp[1]), inf);
dp[0][s] = du[s];
dp[1][s] = dv[s];
vector<int> d(n, inf);
d[s] = 0;
priority_queue<ar<int, 2>, vector<ar<int, 2>>, greater<>> pq;
pq.push({0, s});
while(!pq.empty()) {
auto [d_v, v] = pq.top();
pq.pop();
if(d_v != d[v]) continue;
for(auto [to, w] : adj[v]) {
if( d[to] > d[v] + w ) {
d[to] = d[v] + w;
dp[0][to] = min(dp[0][v], du[to]);
dp[1][to] = min(dp[1][v], dv[to]);
pq.push({d[to], to});
} else if( d[to] == d[v] + w ) {
if( dp[0][to] + dp[1][to] > min(du[to], dp[0][v]) + min(dv[to], dp[1][v]) ) {
dp[0][to] = min(dp[0][v], du[to]);
dp[1][to] = min(dp[1][v], dv[to]);
}
}
}
}
chmin(ans, dp[0][t] + dp[1][t]);
};
D2(S, T), D2(T, S);
cout << ans << nl;
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
solve();
}
