#include <bits/stdc++.h>
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math,O3")
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization("unroll-loops")
#pragma ("reroll")
#define skip continue;
#define gold ios_base::sync_with_stdio(false);cin.tie(NULL);
#define xa "\n"
#define int long long
#define all(a) a.begin(), a.end()
#define pb push_back
using namespace std;
const int mod = 1e9 + 7;
const int N = 2e5 + 7;
const int MAX = 1e9;
const int inf = 1e18;
int gcd(int a, int b) { if (b == 0) return a; else if(a == 0) return b; else return gcd(b, a % b); }
int lcm(int a, int b) { return a / gcd(a, b) * b; }
vector <pair < int, int > > g[N];
int n, m, dist[N];
int parent[N];
int x[N], y[N], w[N];
map < pair < int, int >, int > check;
void dijkstra(int start) {
for(int i = 1; i <= n; i++){
parent[i] = 0;
dist[i] = inf;
}
set < pair < int ,int > > st;
dist[start] = 0, st.insert({ 0, start });
while(st.size() > 0) {
int v = (*st.begin()).second;
st.erase(st.begin());
for (auto p : g[v]) {
int to = p.first, w = p.second;
if (dist[v] + w < dist[to]) {
parent[to] = v;
st.erase({ dist[to], to });
dist[to] = dist[v] + w;
st.insert({ dist[to], to });
}
}
}
}
void solve() {
cin >> n >> m;
int s, t;
cin >> s >> t;
int u, v;
cin >> u >> v;
for(int i = 1; i <= m; i++){
cin >> x[i] >> y[i] >> w[i];
g[x[i]].pb({y[i], w[i]});
g[y[i]].pb({x[i], w[i]});
}
dijkstra(s);
int one = t, two = parent[t];
for(int i = 1; i <= n; i++){
g[i].clear();
}
while(two != 0){
g[two].pb({one, 0});
g[one].pb({two, 0});
check[{one, two}] = 1;
check[{two, one}] = 1;
one = parent[one];
two = parent[two];
}
for(int i = 1; i <= m; i++){
if(check[{x[i], y[i]}] == 0){
g[x[i]].pb({y[i], w[i]});
g[y[i]].pb({x[i], w[i]});
}
}
dijkstra(u);
cout << dist[v];
}
signed main() {
gold;
//freopen("pails.in", "r", stdin);
//freopen("pails.out", "w", stdout);
int t = 1;
int ti = 1;
//cin >> t;
while (t--) {
//cout << "Case " << ti << ": ";
solve();
ti++;
}
}
