#include <iostream>
#include <queue>
#include <limits>
using namespace std;
vector<pair<int, long long>> edges[100001];
long long u_distances[100001];
long long best_entry[100001];
long long best_finished[100001];
long long rbest_entry[100001];
long long rbest_finished[100001];
long long v_distances[100001];
long long s_distances[100001];
int n, m, s, t, u, v, a, b;
long long c;
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n >> m >> s >> t >> u >> v;
while (m--){
cin >> a >> b >> c;
edges[a].emplace_back(b, c);
edges[b].emplace_back(a, c);
}
for (int i = 1; i <= n; i++){
u_distances[i] = numeric_limits<long long>::max();
}
u_distances[u] = 0;
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<>> q1;
q1.emplace(0, u);
while (!q1.empty()){
long long d1 = q1.top().first;
long long node = q1.top().second;
q1.pop();
if (u_distances[node]!=d1){
continue;
}
for (auto [connected, length] : edges[node]){
if (d1 + length < u_distances[connected]){
u_distances[connected] = d1+length;
q1.emplace(d1+length, connected);
}
}
}
for (int i = 1; i <= n; i++){
v_distances[i] = numeric_limits<long long>::max();
}
v_distances[v] = 0;
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<>> q2;
q2.emplace(0, v);
while (!q2.empty()){
long long d1 = q2.top().first;
long long node = q2.top().second;
q2.pop();
if (v_distances[node]!=d1){
continue;
}
for (auto [connected, length] : edges[node]){
if (d1 + length < v_distances[connected]){
v_distances[connected] = d1+length;
q2.emplace(d1+length, connected);
}
}
}
for (int i = 1; i <= n; i++){
s_distances[i] = numeric_limits<long long>::max();
best_entry[i] = numeric_limits<long long>::max();
best_finished[i] = numeric_limits<long long>::max();
rbest_entry[i] = numeric_limits<long long>::max();
rbest_finished[i] = numeric_limits<long long>::max();
}
s_distances[s] = 0;
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<>> q3;
q3.emplace(0, s);
while (!q3.empty()){
long long d1 = q3.top().first;
long long node = q3.top().second;
q3.pop();
if (s_distances[node]!=d1){
continue;
}
best_entry[node] = min(best_entry[node], u_distances[node]);
best_finished[node] = min(best_finished[node], v_distances[node] + best_entry[node]);
rbest_entry[node] = min(rbest_entry[node], v_distances[node]);
rbest_finished[node] = min(rbest_finished[node], u_distances[node] + rbest_entry[node]);
for (auto [connected, length] : edges[node]){
if (d1 + length < s_distances[connected]){
s_distances[connected] = d1 + length;
q3.emplace(d1+length, connected);
best_entry[connected] = best_entry[node];
best_finished[connected] = best_finished[node];
rbest_entry[connected] = rbest_entry[node];
rbest_finished[connected] = rbest_finished[node];
}
else if (d1 + length == s_distances[connected]){
best_entry[connected] = min(best_entry[node], best_entry[connected]);
best_finished[connected] = min(best_finished[node], best_finished[connected]);
rbest_entry[connected] = min(rbest_entry[node], rbest_entry[connected]);
rbest_finished[connected] = min(rbest_finished[node], rbest_finished[connected]);
}
}
}
cout << min(min(best_finished[t], rbest_finished[t]), u_distances[v]);
}
