#define taskname "cumm"
#include <bits/stdc++.h>
using namespace std;
const int kN = 1e5 + 1;
const long long kInf = 5e18;
int n, m, s, t, u, v;
long long dp[2][kN];
vector<pair<int, long long>> g[kN];
void Dijkstra(int s, vector<long long>& x, int i, vector<long long>& f) {
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> pq;
x.resize(n + 1, kInf);
x[s] = 0;
pq.push({x[s], s});
vector<bool> y(n + 1, false);
while (!pq.empty()) {
auto a = pq.top();
pq.pop();
if (y[a.second]) {
continue;
}
y[a.second] = true;
for (auto [b, w] : g[a.second]) {
if (x[b] > x[a.second] + w) {
x[b] = x[a.second] + w;
if (i != -1) {
dp[i][b] = min(dp[i][a.second], f[a.second]);
}
pq.push({x[b], b});
} else if (x[a.second] + w == x[b] && i != -1) {
dp[i][b] = min(dp[i][b], min(dp[i][a.second], f[a.second]));
}
}
}
}
int main() {
if (fopen(taskname".txt", "r")) {
freopen(taskname".txt", "r", stdin);
freopen(taskname".out", "w", stdout);
}
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1; i <= m; i++) {
int a, b, c;
cin >> a >> b >> c;
g[a].push_back({b, c});
g[b].push_back({a, c});
}
for (int i = 0; i <= n; i++) {
dp[0][i] = dp[1][i] = kInf;
}
vector<long long> du, dv, ds, dt, k = {0};
Dijkstra(u, du, -1, k);
Dijkstra(v, dv, -1, k);
Dijkstra(s, ds, 0, dv);
Dijkstra(t, dt, 1, dv);
long long result = du[v];
for (int i = 1; i <= n; i++) {
if (ds[i] + dt[i] == ds[t]) {
result = min(result, min(dp[0][i], dp[1][i]) + du[i]);
}
}
cout << result;
return 0;
}
