#include <bits/stdc++.h>
using namespace std;
constexpr int64_t INF = 0x3f3f3f3f3f3f3f3f;
struct min_heap_elem {
int64_t d;
int u;
min_heap_elem(int64_t d, int u) : d(d), u(u) {}
bool operator<(const min_heap_elem& rhs) const {
return d > rhs.d;
}
};
struct max_heap_elem {
int64_t d;
int u;
max_heap_elem(int64_t d, int u) : d(d), u(u) {}
bool operator<(const max_heap_elem& rhs) const {
return d < rhs.d;
}
};
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
#ifdef home
freopen("in", "r", stdin);
freopen("out", "w", stdout);
#endif
int n, m, s, t, m1, m2;
cin >> n >> m >> s >> t >> m1 >> m2;
--s, --t, --m1, --m2;
vector<vector<pair<int, int>>> adj(n);
for (int u, v, w; m--;) {
cin >> u >> v >> w, --u, --v;
adj[u].emplace_back(w, v);
adj[v].emplace_back(w, u);
}
auto dijk = [&](int src) {
vector<int64_t> dist(n, INF);
priority_queue<min_heap_elem> pq;
pq.emplace(dist[src] = 0, src);
while (!pq.empty()) {
const auto [d, u] = pq.top();
pq.pop();
if (d != dist[u]) continue;
for (const auto& [w, v] : adj[u])
if (dist[v] > d + w)
pq.emplace(dist[v] = d + w, v);
}
return dist;
};
auto dist = dijk(s);
auto dist_from_u = dijk(m1), dist_from_v = dijk(m2);
auto solve = [&](vector<int64_t>& dp1, vector<int64_t>&& dp2) {
vector<bool> visited(n);
visited[t] = true;
priority_queue<max_heap_elem> pq;
pq.emplace(dist[t], t);
while (!pq.empty()) {
const auto [d, v] = pq.top();
pq.pop();
for (const auto& [w, u] : adj[v])
if (!visited[u] && d == dist[u] + w) {
visited[u] = true;
dp2[u] = min(dp2[u], dp2[v]);
pq.emplace(dist[u], u);
}
}
int64_t ret = INT64_MAX;
for (int i = 0; i < n; ++i)
ret = min(ret, dp1[i] + dp2[i]);
return ret;
};
cout << min(solve(dist_from_u, move(dist_from_v)),
solve(dist_from_v, move(dist_from_u)));
}
