#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define all(v) v.begin(), v.end()
#define endl '\n'
#define pl(var) " [" << #var << ": " << (var) << "] "
template<typename A, typename B> ostream& operator<<(ostream &cout, pair<A, B> const &p) { return cout << "[" << p.first << ", " << p.second << "]"; }
template<typename A> ostream& operator<<(ostream &cout, vector<A> const &v) { cout << "["; for(ll int i = 0; i < (ll int)v.size(); i++) {if (i) cout << ", "; cout << v[i];} return cout << "]";}
ll int inf = 1e18;
vector<ll int> distancesS, distancesU, distancesV, distances;
vector<vector<pair<ll int, ll int>>> adj;
vector<vector<ll int>> from;
vector<bool> vis;
void djkstra(ll int start) {
fill(all(distances), inf);
distances[start] = 0;
priority_queue<pair<ll int, ll int>> pq;
pq.emplace(0, start);
while (pq.size()) {
ll int node, d;
tie(d, node) = pq.top();
pq.pop();
d = -1 * d;
if (distances[node] != d) continue;
for (auto [v, wt] : adj[node]) {
ll int new_dist = d + wt;
if (new_dist < distances[v]) {
distances[v] = new_dist;
pq.emplace(-new_dist, v);
}
}
}
}
ll int ans = 0;
vector<ll int> mem;
ll int dfs2(ll int u) {
// if (vis[u]) return inf;
if (vis[u]) return mem[u];
// cout << pl(u) << endl;
vis[u] = 1;
ll int mn = inf;
for (ll int v : from[u]) {
mn = min(mn, dfs2(v));
}
ans = min(ans, mn + distancesV[u]);
return mem[u] = min(mn, distancesU[u]);
}
void solve() {
ll int n, m; cin >> n >> m;
ll int s, t; cin >> s >> t; s--, t--;
ll int U, V; cin >> U >> V; U--, V--;
adj.resize(n);
vis.resize(n);
distances.resize(n);
distancesS.resize(n);
distancesU.resize(n);
distancesV.resize(n);
from.resize(n);
mem.resize(n);
fill(all(mem),0);
for (ll int i = 0; i < m; i++) {
ll int a, b, c; cin >> a >> b >> c;
a--, b--;
adj[a].emplace_back(b, c);
adj[b].emplace_back(a, c);
}
// run djkstra
djkstra(U); for (ll int i = 0; i < n; i++) distancesU[i] = distances[i];
djkstra(V); for (ll int i = 0; i < n; i++) distancesV[i] = distances[i];
auto djkstra1 = [&]() {
// I know u and v
fill(all(distancesS), inf);
distancesS[s] = 0;
priority_queue<pair<ll int, ll int>> pq;
pq.emplace(0, s);
while (pq.size()) {
auto [dist, node] = pq.top();
pq.pop();
dist = dist * -1;
if (distancesS[node] != dist) continue;
for (auto [v, wt] : adj[node]) {
ll int new_dist = dist + wt;
if (new_dist < distancesS[v]) {
distancesS[v] = new_dist;
from[v].clear();
from[v].push_back(node);
pq.emplace(-new_dist, v);
} else if (new_dist == distancesS[v]) {
from[v].push_back(node);
}
}
}
};
// cout << pl(distances)
djkstra1();
ans = distancesU[V];
assert(distancesU[V] == distancesV[U]);
dfs2(t);
fill(all(vis), 0);
// change s and v and run dfs2 again
distancesV.swap(distancesU);
fill(all(mem), inf);
dfs2(t);
cout << ans << endl;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
ll int T = 1;
// cin >> T;
while (T--)
solve();
return 0;
}
