#include<bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define int long long
const int MX = 2e5 + 5;
const int MOD = 1e9 + 7;
int n, m, s, t, u, v;
vector<pair<int, int>> adj[MX];
int Ls[MX], Lt[MX];
void dijkstra(int i1, int L[]) {
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> q;
for (int i = 1; i <= n; i++) L[i] = 1e18;
L[i1] = 0;
q.push({L[i1], i1});
while (!q.empty()) {
int u = q.top().se;
int du = q.top().fi;
q.pop();
if (du != L[u]) continue;
for (auto it : adj[u]) {
int v = it.se;
int uv = it.fi;
if (du + uv < L[v]) {
L[v] = du + uv;
q.push({L[v], v});
}
}
}
}
int dp[MX][3]; // 0 chua dung // 1 dang dung` // 2 da~ dung`
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
// int test; cin>>test; while (test--) {}
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1; i <= m; i++) {
int u1, v1, c1;
cin >> u1 >> v1 >> c1;
adj[u1].push_back({c1, v1});
adj[v1].push_back({c1, u1});
}
dijkstra(s, Ls);
dijkstra(t, Lt);
// dp[u][0 1 2]
// dang o dinh u
// 0: chua dung` duong chung
// 1: dang tren duong chung
// 2: da su dung xong duong chung
priority_queue<pair<int, pair<int, int>>, vector<pair<int, pair<int, int>>>, greater<pair<int, pair<int, int>>>> q;
for (int i = 1; i <= n; i++) {
dp[i][0] = dp[i][1] = dp[i][2] = 1e18;
}
dp[u][0] = 0;
q.push({dp[u][0], {u, 0}});
while (!q.empty()) {
int du = q.top().fi;
int u = q.top().se.fi;
int now = q.top().se.se;
q.pop();
if (du != dp[u][now]) continue;
if (now == 0 && dp[u][1] > du) {
dp[u][1] = du;
q.push({dp[u][1], {u, 1}});
}
if (now == 1 && dp[u][2] > du) {
dp[u][2] = du;
q.push({dp[u][2], {u, 2}});
}
for (auto it : adj[u]) {
int v = it.se;
int uv = it.fi;
// dp[v][0];
if (now == 0 || now == 2) {
if (dp[v][now] > du + uv) {
dp[v][now] = du + uv;
q.push({dp[v][now], {v, now}});
}
}
else if (now == 1) {
if (Ls[u] + uv + Lt[v] == Ls[t] && dp[v][1] > du) {
dp[v][1] = du;
q.push({dp[v][1], {v, 1}});
}
}
}
}
int fn = min({dp[v][0], dp[v][1], dp[v][2]});
// cout << dp[v][0] << ' ' << dp[v][1] << ' ' << dp[v][2] << '\n';
for (int i = 1; i <= n; i++) {
dp[i][0] = dp[i][1] = dp[i][2] = 1e18;
}
dp[u][0] = 0;
q.push({dp[u][0], {u, 0}});
while (!q.empty()) {
int du = q.top().fi;
int u = q.top().se.fi;
int now = q.top().se.se;
q.pop();
if (du != dp[u][now]) continue;
if (now == 0 && dp[u][1] > du) {
dp[u][1] = du;
q.push({dp[u][1], {u, 1}});
}
if (now == 1 && dp[u][2] > du) {
dp[u][2] = du;
q.push({dp[u][2], {u, 2}});
}
for (auto it : adj[u]) {
int v = it.se;
int uv = it.fi;
// dp[v][0];
if (now == 0 || now == 2) {
if (dp[v][now] > du + uv) {
dp[v][now] = du + uv;
q.push({dp[v][now], {v, now}});
}
}
else if (now == 1) {
if (Ls[v] + uv + Lt[u] == Ls[t] && dp[v][1] > du) {
dp[v][1] = du;
q.push({dp[v][1], {v, 1}});
}
}
}
}
fn = min({fn, dp[v][0], dp[v][1], dp[v][2]});
cout << fn;
return 0;
}
// binhtinhtutinkhongcaycunhungmotkhikhongcontutinnualatuyetvong
