#include <bits/stdc++.h>
using namespace std;
const long long INF = (long long) 1e18;
template<typename T>
struct edge {
int from, to;
T cost;
};
void calc(int s, vector<long long>& dist, vector<long long>& dp, const vector<long long>& dist2, const vector< vector< edge<long long> > >& g) {
dp.assign((int) g.size(), INF);
dp[s] = dist2[s];
priority_queue< pair<long long, int>, vector< pair<long long, int> >, greater< pair<long long, int> > > pq;
pq.push({0, s});
dist.assign((int) g.size(), INF);
dist[s] = 0;
while (!pq.empty()) {
long long d = pq.top().first;
int u = pq.top().second;
pq.pop();
if (d > dist[u]) {
continue;
}
for (auto& v : g[u]) {
if (d + v.cost < dist[v.to]) {
dist[v.to] = d + v.cost;
pq.push({dist[v.to], v.to});
dp[v.to] = min(dp[u], dist2[v.to]);
}
}
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
vector< vector< edge<long long> > > g(n + 1);
for (int i = 0; i < m; i++) {
int a, b;
long long c;
cin >> a >> b >> c;
g[a].push_back({a, b, c});
g[b].push_back({b, a, c});
}
vector<long long> dist1(n + 1), dist2, dist3, dist4;
vector<long long> dp1, dp2;
calc(u, dist1, dp1, dist1, g);
calc(v, dist2, dp1, dist1, g);
calc(s, dist3, dp1, dist2, g);
calc(t, dist4, dp2, dist2, g);
long long ans = INF;
for (int i = 1; i <= n; i++) {
if (dist3[i] + dist4[i] == dist3[t]) {
ans = min(ans, dist1[i] + min(dp1[i], dp2[i]));
}
}
cout << min(ans, dist1[v]) << '\n';
return 0;
}
