#include <bits/stdc++.h>
#define nl '\n'
template <typename T>
inline bool ckmin(T& x, const T& y) {
return y < x ? x = y, 1 : 0;
}
signed main() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
int N, M, S, T, U, V;
std::cin >> N >> M >> S >> T >> U >> V;
--S, --T, --U, --V;
std::vector<std::vector<std::pair<int, int>>> adj(N);
for (int i = 0; i < M; i++) {
int u, v, w;
std::cin >> u >> v >> w;
--u, --v;
adj[u].emplace_back(v, w);
adj[v].emplace_back(u, w);
}
auto dijkstra = [&](int st) -> std::vector<int64_t> {
std::vector<int64_t> dp(N, 1e18);
dp[st] = 0;
std::priority_queue<std::pair<int64_t, int>> pq;
pq.emplace(dp[st], st);
while (pq.size()) {
auto [d, u] = pq.top();
pq.pop();
d = -d;
if (dp[u] < d) continue;
for (auto [v, w] : adj[u]) {
auto nd = d + w;
if (nd < dp[v]) {
dp[v] = nd;
pq.emplace(-dp[v], v);
}
}
}
return dp;
};
auto dpU = dijkstra(U);
auto dpV = dijkstra(V);
auto dijkstra2 = [&](int st, std::vector<int64_t>& minU,
std::vector<int64_t>& minV) -> std::vector<int64_t> {
std::vector<int64_t> dp(N, 1e18);
dp[st] = 0;
minU.assign(N, 1e18);
minV.assign(N, 1e18);
std::priority_queue<std::pair<int64_t, int>> pq;
pq.emplace(dp[st], st);
while (pq.size()) {
auto [d, u] = pq.top();
pq.pop();
d = -d;
if (dp[u] < d) continue;
ckmin(minU[u], dpU[u]);
ckmin(minV[u], dpV[u]);
for (auto [v, w] : adj[u]) {
auto nd = d + w;
if (nd == dp[v]) {
ckmin(minU[v], minU[u]);
ckmin(minV[v], minV[u]);
} else if (nd < dp[v]) {
minU[v] = minU[u];
minV[v] = minV[u];
dp[v] = nd;
pq.emplace(-dp[v], v);
}
}
}
return dp;
};
std::vector<int64_t> minSU, minSV, minTU, minTV;
auto dpS = dijkstra2(S, minSU, minSV);
auto dpT = dijkstra2(T, minTU, minTV);
int64_t ans = dpU[V];
for (int i = 0; i < N; i++) {
if (dpS[i] + dpT[i] == dpS[T]) {
// this is an edge
ckmin(ans, minSU[i] + minTV[i]);
ckmin(ans, minSV[i] + minTU[i]);
}
}
std::cout << ans << nl;
}
