#include <bits/stdc++.h> // NeOWami
using namespace std;
#define ft first
#define sc second
#define int long long
using pii = pair<int, int>;
template<class T> using heapmin = priority_queue<T, vector<T>, greater<T>>;
const int N = 1e5 + 5;
const int inf = 1e17;
int n, m, s, t, u, v;
vector<pii> G[N];
int sdist[N], tdist[N], udist[N], vdist[N];
int min_dist_from_v_to_i_reliant_on_s[N], min_dist_from_v_to_i_reliant_on_t[N];
bool ckmin(int &u, int v) {
if (u > v) return u = v, 1;
return 0;
}
void dijkstra(int root, int dist[]) {
for (int i = 1; i <= n; i++) dist[i] = inf;
dist[root] = 0;
heapmin<pii> Q;
Q.push({0, root});
while(!Q.empty()) {
int old = Q.top().ft, u = Q.top().sc;
Q.pop();
if (old != dist[u]) continue;
for (pii item: G[u]) {
int w = item.ft + old, v = item.sc;
if (ckmin(dist[v], w)) Q.push({dist[v], v});
}
}
}
void calc(int root, int dist[], const int cost[], int min_cost[], int tar) {
for (int i = 1; i <= n; i++) dist[i] = min_cost[i] = inf;
dist[root] = 0;
heapmin<pii> Q;
Q.push({0, root});
min_cost[root] = cost[root];
while(!Q.empty()) {
int old = Q.top().ft, u = Q.top().sc;
Q.pop();
if (old != dist[u]) continue;
if (u == tar) break;
for (pii item: G[u]) {
int w = item.ft + old, v = item.sc;
if (ckmin(dist[v], w)) {
Q.push({dist[v], v});
min_cost[v] = min(min_cost[u], cost[v]);
}
else if (dist[v] == w) {
min_cost[v] = min({min_cost[v], min_cost[u], cost[v]});
}
}
}
}
signed main() {
cin.tie(NULL)->sync_with_stdio(false);
if(ifstream("Input.inp")) {
freopen("Input.inp", "r", stdin);
freopen("Output.out", "w", stdout);
}
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1; i <= m; i++) {
int u, v, w; cin >> u >> v >> w;
G[u].push_back({w, v});
G[v].push_back({w, u});
}
dijkstra(u, udist);
dijkstra(v, vdist);
calc(s, sdist, vdist, min_dist_from_v_to_i_reliant_on_s, t);
calc(t, tdist, vdist, min_dist_from_v_to_i_reliant_on_t, s);
int ans = udist[v];
for (int i = 1; i <= n; i++) {
if (sdist[i] + tdist[i] == sdist[t]) {
ans = min(ans, udist[i] + min(min_dist_from_v_to_i_reliant_on_s[i], min_dist_from_v_to_i_reliant_on_t[i]));
}
}
cout << ans;
return 0;
}
