#include "bits/stdc++.h"
using namespace std;
struct node {
int v;
long long dist, mtu, mtv;
bool operator<(const node &rhs) const {
if (dist == rhs.dist)
return mtu + mtv < rhs.mtu + rhs.mtv;
return dist > rhs.dist;
}
};
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
int N, M, S, T, U, V;
cin >> N >> M >> S >> T >> U >> V;
vector<pair<int, long long>> adj[N + 1];
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});
}
auto distcalc = [&](int s) {
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> q;
vector<long long> dist(N + 1, 1e18);
vector<bool> vis(N + 1);
q.push({0, s});
while (!q.empty()) {
pair<long long, int> v = q.top();
q.pop();
if (vis[v.second]) continue;
vis[v.second] = true;
dist[v.second] = v.first;
for (auto u : adj[v.second]) {
q.push({u.second + v.first, u.first});
}
}
return dist;
};
vector<long long> fu = distcalc(U), fv = distcalc(V);
priority_queue<node> q;
vector<long long> dist(N + 1, 1e18);
q.push({S, 0, fu[S], fv[S]});
long long bt = -1, ans = 1e18;
while (!q.empty()) {
node v = q.top();
q.pop();
if (v.v == T) {
if (bt == -1)
bt = v.dist;
if (bt == v.dist)
ans = min(ans, v.mtu + v.mtv);
}
if (dist[v.v] < v.dist) continue;
dist[v.v] = v.dist;
for (auto u : adj[v.v]) {
q.push({u.first, v.dist + u.second, min(v.mtu, fu[u.first]), min(v.mtv, fv[u.first])});
}
}
cout << min(ans, fu[V]) << '\n';
}
