#include <bits/stdc++.h>
using namespace std;
string to_string(string s) {
return '"' + s + '"';
}
string to_string(const char* s) {
return to_string((string) s);
}
string to_string(bool b) {
return (b ? "true" : "false");
}
template <typename A, typename B>
string to_string(pair<A, B> p) {
return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A>
string to_string(A v) {
bool first = true;
string res = "{";
for (const auto &x : v) {
if (!first) {
res += ", ";
}
first = false;
res += to_string(x);
}
res += "}";
return res;
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
cerr << " " << to_string(H);
debug_out(T...);
}
#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif
#define int long long
int32_t main() {
if (fopen("input.txt", "r")) {
freopen("input.txt", "r", stdin);
}
cin.tie(0)->sync_with_stdio(0);
using ii = pair<int, int>;
int n, m, S, T, U, V; cin >> n >> m >> S >> T >> U >> V;
vector<vector<ii>> ad(n + 1);
for (int i = 0; i < m; ++i) {
int u, v, c; cin >> u >> v >> c;
ad[u].push_back({v, c});
ad[v].push_back({u, c});
}
vector<int> fs(n + 1), ft(n + 1), fu(n + 1), fv(n + 1);
function dijkstra = [&](int u, vector<int> &f) {
fill(f.begin(), f.end(), 1e14);
priority_queue<ii, vector<ii>, greater<ii>> q;
q.push({f[u] = 0, u});
while (q.size()) {
auto [w, u] = q.top(); q.pop();
for (auto [v, c] : ad[u]) {
if (f[v] > w + c) {
f[v] = w + c;
q.push({f[v], v});
}
}
}
};
dijkstra(S, fs);
dijkstra(T, ft);
dijkstra(U, fu);
dijkstra(V, fv);
int answer = LLONG_MAX;
for (int i = 0; i < 2; ++i) {
vector<vector<int>> f(n + 1, vector<int>(2, 1e14));
using iii = tuple<int, int, int>;
priority_queue<iii, vector<iii>, greater<iii>> q;
q.push(make_tuple(f[U][0] = 0, U, 0));
while (q.size()) {
auto [w, u, s] = q.top(); q.pop();
answer = min(answer, w + fv[u]);
for (auto [v, c] : ad[u]) {
auto onpath = fs[u] + c + ft[v] == fs[T];
if (f[v][s] > w + c) {
f[v][s] = w + c;
q.push(make_tuple(f[v][s], v, s));
}
if (onpath && f[v][1] > w) {
f[v][1] = w;
q.push(make_tuple(f[v][1], v, 1));
}
}
}
swap(U, V); swap(fu, fv);
}
cout << answer << '\n';
}
