#include <bits/stdc++.h>
using namespace std;
const long long INF = (long long) 1e18;
template<typename T>
struct edge {
int from, to;
T cost;
};
void dijkstra(const vector< vector< edge<long long> > >& g, int s, vector<long long>& dist, vector< vector<int> >& newG) {
dist.assign((int) g.size(), INF);
dist[s] = 0;
newG.assign((int) g.size(), {});
priority_queue< pair<long long, int>, vector< pair<long long, int> >, greater< pair<long long, int> > > pq;
pq.push({0, s});
while (!pq.empty()) {
long long d = pq.top().first;
int u = pq.top().second;
pq.pop();
if (d < dist[u]) {
continue;
}
for (auto& v : g[u]) {
if (d + v.cost < dist[v.to]) {
dist[v.to] = d + v.cost;
pq.push({dist[v.to], v.to});
newG[u].push_back(v.to);
}
}
}
}
void calc_dp(const vector< vector<int> >& g, const vector<long long>& dist, int s, vector<long long>& dp) {
queue<int> que;
que.push(s);
dp.assign((int) g.size(), INF);
dp[s] = dist[s];
vector<int> was((int) g.size(), 0);
was[s] = 0;
while (!que.empty()) {
int u = que.front();
que.pop();
for (auto& v : g[u]) {
if (!was[v]) {
que.push(v);
dp[v] = min(dp[u], dist[v]);
was[v] = 1;
}
}
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
vector< vector< edge<long long> > > g(n + 1);
for (int i = 0; i < m; i++) {
int a, b;
long long c;
cin >> a >> b >> c;
g[a].push_back({a, b, c});
g[b].push_back({b, a, c});
}
vector<long long> dist_u, dist_v, dist_s, dist_t, dp1, dp2;
vector< vector<int> > g_s, g_t;
dijkstra(g, u, dist_u, g_s);
dijkstra(g, v, dist_v, g_s);
dijkstra(g, s, dist_s, g_s);
dijkstra(g, t, dist_t, g_t);
calc_dp(g_s, dist_v, s, dp1);
calc_dp(g_t, dist_v, t, dp2);
long long ans = INF;
for (int i = 1; i <= n; i++) {
if (dist_s[i] + dist_t[i] == dist_s[t]) {
ans = min(ans, dist_u[i] + min(dp1[i], dp2[i]));
}
}
cout << min(ans, dist_u[v]) << '\n';
return 0;
}
