#include <bits/stdc++.h>
#define pii pair<ll, ll>
typedef long long ll;
using namespace std;
const int MAX = 100007;
vector<pii> G[MAX];
ll D[MAX], inQ[MAX], C[2][MAX];
pii dp[MAX];
void Dijkstra(int S, int N, ll* D) {
priority_queue<pii, vector<pii>, greater<pii>> PQ;
PQ.emplace(D[S] = 0, S);
while (!PQ.empty()) {
auto [cd, cur] = PQ.top(); PQ.pop();
if (cd > D[cur]) continue;
for (auto& [next, nd] : G[cur]) {
if (cd + nd >= D[next]) continue;
PQ.emplace(D[next] = cd + nd, next);
}
}
}
int main() {
ios::sync_with_stdio(0); cin.tie(0);
int N, M, S, T, U, V;
cin >> N >> M >> S >> T >> U >> V;
for (int i = 1; i <= M; ++i) {
int u, v, c;
cin >> u >> v >> c;
G[u].emplace_back(v, c);
G[v].emplace_back(u, c);
}
memset(D, 0x3f, sizeof(D));
Dijkstra(S, N, D);
memset(C, 0x3f, sizeof(C));
Dijkstra(U, N, C[0]);
Dijkstra(V, N, C[1]);
ll ans = C[0][V];
fill(dp, dp + MAX, make_pair(1e18, 1e18));
priority_queue<pii> PQ;
PQ.emplace(D[T], T);
while (!PQ.empty()) {
auto [cd, cur] = PQ.top(); PQ.pop();
ans = min(ans, C[0][cur] + dp[cur].second);
ans = min(ans, C[1][cur] + dp[cur].first);
dp[cur].first = min(dp[cur].first, C[0][cur]);
dp[cur].second = min(dp[cur].second, C[1][cur]);
for (auto& [next, d] : G[cur]) {
if (D[next] + d != D[cur]) continue;
if (!inQ[next]) {
PQ.emplace(D[next], next);
inQ[next] = 1;
}
dp[next].first = min(dp[next].first, dp[cur].first);
dp[next].second = min(dp[next].second, dp[cur].second);
}
}
cout << ans;
return 0;
}
