#include <bits/stdc++.h>
using namespace std;
vector<int> last;
set<pair<int, int>> choosenE;
vector<long long> dijkstra(int start, vector<vector<pair<int, int>>>& g) {
int n = g.size();
vector<long long> d(n, numeric_limits<long long>::max());
last.assign(n, -1);
d[start] = 0;
set<pair<long long, int>> s; // {d[i], i}
s.insert({0, start});
while (!s.empty()) {
int i = s.begin()->second;
s.erase(s.begin());
for (auto [j, w] : g[i]) {
if (d[i] + w < d[j]) {
s.erase({d[j], j});
d[j] = d[i] + w;
last[j] = i;
s.insert({d[j], j});
}
}
}
return d;
}
vector<long long> dijkstra2(int start, vector<vector<pair<int, int>>>& g) {
int n = g.size();
vector<long long> d(n, numeric_limits<long long>::max());
last.assign(n, -1);
d[start] = 0;
set<pair<long long, int>> s; // {d[i], i}
s.insert({0, start});
while (!s.empty()) {
int i = s.begin()->second;
s.erase(s.begin());
for (auto [j, w] : g[i]) {
if (choosenE.find({i, j}) != choosenE.end() || choosenE.find({j, i}) != choosenE.end()) {
w = 0;
}
if (d[i] + w < d[j]) {
s.erase({d[j], j});
d[j] = d[i] + w;
last[j] = i;
s.insert({d[j], j});
}
}
}
return d;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int n, m;
cin >> n >> m;
int s, t;
cin >> s >> t;
--s, --t;
int u, v;
cin >> u >> v;
--u, --v;
vector<vector<pair<int, int>>> g(n);
for (int _m = 0; _m < m; ++_m) {
int a, b, w;
cin >> a >> b >> w;
--a, --b;
g[a].push_back({b, w});
g[b].push_back({a, w});
}
dijkstra(s, g);
while (t >= 0) {
choosenE.insert({last[t], t});
t = last[t];
}
auto d = dijkstra2(u, g);
cout << d[v] << '\n';
return 0;
}
