#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
const ll INF = 2e18;
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
ll n, m, s, t, u, v; cin >> n >> m >> s >> t >> u >> v;
vector<vector<pll>> g(n + 1);
while (m--) {
ll u, v, w; cin >> u >> v >> w;
g[u].push_back({v, w});
g[v].push_back({u, w});
}
vector<ll> d(n + 1, INF), p(n + 1, -1); d[s] = 0; p[s] = s;
set<pll> q; for (ll u = 1; u <= n; u++) q.insert({ d[u], u });
while (!q.empty()) {
auto [_, u] = *q.begin();
q.erase(q.begin());
for (auto [v, w]: g[u])
if (d[u] + w < d[v]) {
q.erase(q.find({d[v], v}));
d[v] = d[u] + w;
p[v] = u;
q.insert({d[v], v});
}
}
vector<ll> path;
ll curr = t;
while (curr != p[curr]) {
path.push_back(curr);
curr = p[curr];
}
path.push_back(curr);
reverse(path.begin(), path.end());
set<pll> zeros;
for (ll i = 1; i < path.size(); i++)
zeros.insert({path[i], path[i - 1]}),
zeros.insert({path[i - 1], path[i]});
vector<vector<pll>> g2(n + 1);
for (ll u = 1; u <= n; u++)
for (auto [v, w]: g[u])
if (zeros.count({u, v})) g2[u].push_back({v, 0});
else g2[u].push_back({v, w});
vector<ll> d2(n + 1, INF); d2[u] = 0;
set<pll> q2; for (ll u = 1; u <= n; u++) q2.insert({d2[u], u});
while (!q2.empty()) {
auto [_, u] = *q2.begin();
q2.erase(q2.begin());
for (auto [v, w]: g2[u])
if (d2[u] + w < d2[v]) {
q2.erase(q2.find({d2[v], v}));
d2[v] = d2[u] + w;
q2.insert({d2[v], v});
}
}
cout << d2[v];
}
