#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<ll, ll>;
int n, m, s, t, uu, vv, x, y, z;
int main() {
scanf("%d %d %d %d %d %d", &n, &m, &s, &t, &uu, &vv);
vector<vector<pii>> v(n + 5, vector<pii>());
vector<ll> d(n + 5, 1e18), d2(n + 5, 1e18);
ll ans = 1e18;
for (int i = 0; i < m; i++) {
scanf("%d %d %d", &x, &y, &z);
v[x].emplace_back(y, z);
v[y].emplace_back(x, z);
}
auto dijk = [&] (int st, vector<ll> &dist) {
priority_queue<pii, vector<pii>, greater<pii>> pq;
pq.emplace(dist[st] = 0, st);
while (!pq.empty()) {
auto [nd, nn] = pq.top(); pq.pop();
for (auto &[tn, td]: v[nn]) {
if (dist[tn] > dist[nn] + td) pq.emplace(dist[tn] = dist[nn] + td, tn);
}
}
};
auto dijk2 = [&] (int st, int ed) {
priority_queue<pii, vector<pii>, greater<pii>> pq;
vector<ll> dist(n + 5, 1e18);
vector<vector<ll>> dp(2, vector<ll>(n + 5, 1e18));
pq.emplace(dist[st] = 0, st);
while (!pq.empty()) {
auto [nd, nn] = pq.top(); pq.pop();
for (auto &[tn, td]: v[nn]) {
ll xx0 = min(dp[0][nn], d[tn]), xx1 = min(dp[1][nn], d2[tn]);
if (dist[tn] > dist[nn] + td) {
dp[0][tn] = xx0;
dp[1][tn] = xx1;
pq.emplace(dist[tn] = dist[nn] + td, tn);
} else if (dist[tn] == dist[tn] + td && xx0 + xx1 <= dp[0][tn] + dp[1][tn]) {
dp[0][tn] = xx0;
dp[1][tn] = xx1;
}
}
}
ans = min(ans, dp[0][ed] + dp[1][ed]);
};
dijk(uu, d);
dijk(vv, d2);
ans = min(ans, d[vv]);
dijk2(s, t);
dijk2(t, s);
printf("%lld", ans);
}
