#include <bits/stdc++.h>
#define sz(x) (int)x.size()
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define int long long
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
const int mod = 1e9 + 7;
const int LOG = 20;
const int maxn = 1e5 + 5;
const double eps = 1e-9;
int32_t main() {
int n, m, s, t, U, V;
cin >> n >> m >> s >> t >> U >> V;
vector<vector<pii> > graph(n+1);
for(int i=0; i<m; i++) {
int a, b, w;
cin >> a >> b >> w;
graph[a].push_back({ b, w });
graph[b].push_back({ a, w });
}
vector<vector<ll> > dist(3, vector<ll>(n+1, 1e18));
auto dijkstra = [&](int start, int id) {
vector<bool> vis(n+1);
priority_queue<pll, vector<pll>, greater<pll> > pq;
dist[id][start] = 0;
pq.push({ 0, start });
while(!pq.empty()) {
int u = pq.top().second;
pq.pop();
if(vis[u]) continue;
vis[u] = 1;
for(auto &[v, w] : graph[u]) {
if(dist[id][v] > dist[id][u] + w) {
dist[id][v] = dist[id][u] + w;
pq.push({ dist[id][v], v });
}
}
}
};
dijkstra(s, 0); dijkstra(t, 1);
ll SP = dist[0][t];
auto lies_on_sp = [&](int u, int v, int w) {
ll cost1 = dist[0][u] + dist[1][v] + w;
ll cost2 = dist[1][u] + dist[0][v] + w;
return min(cost1, cost2) == SP;
};
vector<bool> vis(n+1);
priority_queue<pll, vector<pll>, greater<pll> > pq;
pq.push({ 0, U });
dist[2][U] = 0;
while(!pq.empty()) {
int u = pq.top().second;
pq.pop();
if(vis[u]) continue;
vis[u] = 1;
for(auto &[v, w] : graph[u]) {
ll cost = (lies_on_sp(u, v, w) ? 0 : w);
if(dist[2][v] > dist[2][u] + cost) {
dist[2][v] = dist[2][u] + cost;
pq.push({ dist[2][v], v });
}
}
}
cout << dist[2][V] << '\n';
return 0;
}
