#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 1e5+1;
vector<pair<int, int>> adj[N];
ll ds[N], du[N], dv[N], minu[N], minv[N], ans[N];
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n, m, s, t, u, v;
cin >> n >> m
>> s >> t
>> u >> v;
while (m--) {
int a, b, c; cin >> a >> b >> c;
adj[a].emplace_back(b, c);
adj[b].emplace_back(a, c);
}
auto dijkstra = [&](int start, ll(&dist)[N], bool store = false) {
for (int i = 1; i <= n; i++)
dist[i] = 1e18;
dist[start] = 0;
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater< >> pq;
pq.emplace(0, start);
while(!pq.empty()) {
auto[d, a] = pq.top();
pq.pop();
if(d != dist[a])
continue;
if(store)
ans[a] = min({ans[a], minu[a] + dv[a], minv[a] + du[a]});
for(auto&[b, c] : adj[a]) {
ll cost = d + c;
if(cost < dist[b]) {
dist[b] = cost;
pq.emplace(cost, b);
if(store) {
minu[b] = min(du[b], minu[a]);
minv[b] = min(dv[b], minv[a]);
ans[b] = ans[a];
}
} else if(store && cost == dist[b]) {
minu[b] = min(minu[b], minu[a]);
minv[b] = min(minv[b], minv[a]);
ans[b] = min(ans[b], ans[a]);
}
}
}
};
dijkstra(u, du);
dijkstra(v, dv);
minu[s] = du[s];
minv[s] = dv[s];
ans[s] = du[s] + dv[s];
dijkstra(s, ds, true);
cout << min(du[v], ans[t]) << '\n';
}
