#include <iostream>
#include <vector>
#include <queue>
using namespace std;
vector<pair<int, long long int>> g[100005];
long long int n, f[5][100005], d[2][100005];
void dijkstra(int j, int x) {
for (int i = 1; i <= n; i++) {
f[j][i] = 1e18;
}
f[j][x] = 0;
priority_queue<pair<long long int, int>> q;
q.push({0, x});
while (!q.empty()) {
long long int x = -q.top().first, u = q.top().second;
q.pop();
if (f[j][u] != x) continue;
for (auto w : g[u]) {
if (f[j][w.first] > f[j][u] + w.second) {
f[j][w.first] = f[j][u] + w.second;
q.push({-f[j][w.first], w.first});
}
}
}
}
long long int dijkstra2(int j, int s, int t) {
for (int i = 1; i <= n; i++) {
f[j][i] = 1e18;
d[0][i] = f[0][i]; d[1][i] = f[1][i];
}
f[j][s] = 0;
priority_queue<pair<long long int, int>> q;
q.push({0, s});
while (!q.empty()) {
long long int x = -q.top().first, u = q.top().second;
q.pop();
if (f[j][u] != x) continue;
for (auto w : g[u]) {
if (f[j][w.first] > f[j][u] + w.second) {
f[j][w.first] = f[j][u] + w.second;
q.push({-f[j][w.first], w.first});
d[0][w.first] = min(f[0][w.first], d[0][u]);
d[1][w.first] = min(f[1][w.first], d[1][u]);
}
else if (f[j][w.first] == f[j][u] + w.second) {
if (min(f[0][w.first], d[0][u]) + min(f[1][w.first], d[1][u]) < d[0][w.first] + d[1][w.first]) {
d[0][w.first] = min(f[0][w.first], d[0][u]);
d[1][w.first] = min(f[1][w.first], d[1][u]);
}
}
}
}
return d[0][t] + d[1][t];
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
int m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1; i <= m; i++) {
int u, v, x;
cin >> u >> v >> x;
g[u].push_back({v, x});
g[v].push_back({u, x});
}
dijkstra(0, u);
dijkstra(1, v);
long long int res = min(f[0][v], dijkstra2(2, s, t));
cout << res;
}
