#include <bits/stdc++.h>
using namespace std;
#define int long long
#define fi first
#define se second
#define pii pair<int, int>
const int maxn = 1e5 + 5;
vector<pii> adj[maxn];
int du[maxn], dv[maxn], dist[maxn], dp[2][maxn], ans;
bool vis[maxn];
//dijkstra 1 tinh du (du[i] = shortest path tu u toi i) tuong tu voi dv;
void dijkstra1(int start, int arr[]) {
for(int i = 0; i < maxn; i++) vis[i] = false;
priority_queue<pair<int, int>> pq;
pq.push({0, start});
while (!pq.empty()) {
int w = pq.top().fi, u = pq.top().se;
pq.pop();
if (!vis[u]) {
arr[u] = -w;
vis[u] = true;
for (pii v: adj[u]) pq.push({w - v.se, v.fi});
}
}
}
void dijkstra2(int start, int end) {
for(int i = 0; i < maxn; i++){
vis[i] = false;
dp[0][i] = dp[1][i] = 1e18;
}
priority_queue<pair<int, pair<int, int>>> pq;
pq.push({0, {start, 0}});
//dung dijkstra duyet qua shortest path s -> t va t -> s
//goi dp[0][i] la shortest path khi xoa 1 vai canh cua shortest path tu s => t hoac t => s va tu u => i
//ket qua la min du[u](di tu u-> i) hoac xoa canh par - u vi nam tren duong di ngan nhat
while (!pq.empty()) {
int c = pq.top().fi, u = pq.top().se.fi, par = pq.top().se.se;
pq.pop();
if (!vis[u]) {
vis[u] = true;
dist[u] = -c;
dp[0][u] = min(du[u], dp[0][par]);
dp[1][u] = min(dv[u], dp[1][par]);
for (pii v: adj[u]) pq.push({c - v.se, {v.fi, u}});
}
//neu ton tai 1 duong di khac toi u co bang do dai thi ta so sanh min va lay ket qua
else if (-c == dist[u]) {
if (min(du[u], dp[0][par]) + min(dv[u], dp[1][par]) <= dp[0][u] + dp[1][u]) {
dp[0][u] = min(du[u], dp[0][par]);
dp[1][u] = min(dv[u], dp[1][par]);
}
}
}
ans = min(ans, dp[0][end] + dp[1][end]);
}
void solve(){
int n, m, s, t, u, v; cin >> n >> m >> s >> t >> u >> v;
for (int i = 1; i <= m; i++) {
int a, b, c; cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
dijkstra1(u, du);
dijkstra1(v, dv);
ans = du[v];
dijkstra2(s, t);
dijkstra2(t, s);
cout << ans;
}
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
int t = 1;
//cin >> t;
while(t--) solve();
//cout << (7 ^ 7);
}
