#include "bits/stdc++.h"
using namespace std;
const long long INF = LLONG_MAX;
template<class T> int id(T x, vector<T> &a) {
return lower_bound(a.begin(), a.end(), x) - a.begin() + 1;
}
int main() {
ios::sync_with_stdio(0), cin.tie(0);
int N, M; cin >> N >> M;
int S, T; cin >> S >> T;
int U, V; cin >> U >> V;
vector<vector<pair<int, int>>> adj(N + 1);
map<pair<int, int>, int> ed;
for (int i = 0; i < M; i++) {
int a, b, c; cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
ed[{a, b}] = ed[{b, a}] = c;
}
auto dijkstra = [](vector<int> S, auto &adj) -> vector<long long> {
const int N = int(size(adj)) - 1;
using T = pair<long long, int>;
priority_queue<T, vector<T>, greater<T>> pq;
vector<long long> dist(N + 1, INF);
auto push = [&](int x, long long d) -> void {
if (d < dist[x])
pq.push({dist[x] = d, x});
};
for (int x : S)
push(x, 0);
while (!pq.empty()) {
auto [d, x] = pq.top(); pq.pop();
if (dist[x] != d) continue;
for (auto [k, dd] : adj[x])
push(k, d + dd);
}
return dist;
};
auto dist_S = dijkstra(vector<int>{S}, adj);
auto dist_T = dijkstra(vector<int>{T}, adj);
auto in_path = [&](int v) -> bool {
return dist_S[v] + dist_T[v] == dist_S[T];
};
auto can_go_S = [&](int x, int y) -> bool {
return dist_S[x] + ed[{x, y}] == dist_S[y] && in_path(x) && in_path(y);
};
auto can_go_T = [&](int x, int y) -> bool {
return dist_T[x] + ed[{x, y}] == dist_T[y] && in_path(x) && in_path(y);
};
vector<pair<int, int>> B;
for (int i = 1; i <= N; i++)
for (int j = 0; j <= 3; j++)
B.push_back({i, j});
vector<vector<pair<int, int>>> g(4 * N + 1);
for (int x = 1; x <= N; x++)
for (auto [k, w] : adj[x]) {
g[id({x, 0}, B)].push_back({id({k, 0}, B), w});
if (in_path(k)) {
g[id({x, 0}, B)].push_back({id({k, 1}, B), w});
g[id({x, 0}, B)].push_back({id({k, 2}, B), w});
}
if (can_go_S(x, k))
g[id({x, 1}, B)].push_back({id({k, 1}, B), 0});
if (can_go_T(x, k))
g[id({x, 2}, B)].push_back({id({k, 2}, B), 0});
if (in_path(x)) {
g[id({x, 1}, B)].push_back({id({k, 3}, B), w});
g[id({x, 2}, B)].push_back({id({k, 3}, B), w});
}
g[id({x, 3}, B)].push_back({id({k, 3}, B), w});
}
vector<int> Z = {id({U, 0}, B)};
if (in_path(U)) {
Z.push_back(id({U, 1}, B));
Z.push_back(id({U, 2}, B));
}
auto d = dijkstra(Z, g);
long long ans = INF;
for (int j = 0; j <= 3; j++)
ans = min(ans, d[id({V, j}, B)]);
cout << ans << '\n';
return 0;
}
