#include <bits/stdc++.h>
using namespace std;
#define int long long
const int N = 1e5;
int n, m, s, t, u, v;
vector<pair<int, int>> adj[N];
int du[N], dv[N], ds[N], dt[N];
void dijkstra(int src, int dist[]) {
fill(dist, dist + N, 1e18);
dist[src] = 0;
priority_queue<pair<int, int>, vector<pair<int, int>>, decltype(greater<>())> pq;
bool done[N] = {};
pq.push({0, src});
while (!pq.empty()) {
int temp = pq.top().second;
pq.pop();
if (done[temp])
continue;
done[temp] = true;
for (auto i : adj[temp]) {
if (dist[i.first] > dist[temp] + i.second) {
dist[i.first] = dist[temp] + i.second;
pq.push({dist[i.first], i.first});
}
}
}
}
int solve() {
dijkstra(u, du);
dijkstra(v, dv);
dijkstra(t, dt);
int mv[N];
fill(mv, mv + N, 1e18);
mv[s] = du[s];
fill(ds, ds + N, 1e18);
ds[s] = 0;
priority_queue<pair<int, int>, vector<pair<int, int>>, decltype(greater<>())> pq;
bool done[N] = {};
pq.push({0, s});
int ans = du[v];
while (!pq.empty()) {
int temp = pq.top().second;
pq.pop();
if (done[temp])
continue;
done[temp] = true;
mv[temp] = min(mv[temp], du[temp]);
if (ds[temp] + dt[temp] == dt[s])
ans = min(ans, mv[temp] + dv[temp]);
for (auto i : adj[temp]) {
if (ds[i.first] > ds[temp] + i.second) {
ds[i.first] = ds[temp] + i.second;
pq.push({ds[i.first], i.first});
mv[i.first] = mv[temp];
} else if (ds[i.first] == ds[temp] + i.second) {
mv[i.first] = min(mv[i.first], mv[temp]);
}
}
}
return ans;
}
void solveTestCase() {
cin >> n >> m >> s >> t >> u >> v;
s--, t--, u--, v--;
for (int i = 0; i < m; i++) {
int a, b, c;
cin >> a >> b >> c;
a--, b--;
adj[a].emplace_back(b, c);
adj[b].emplace_back(a, c);
}
int ans = solve();
swap(u, v);
cout << min(ans, solve());
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
int test = 1;
// cin >> test;
while (test--)
solveTestCase();
}
