// #pragma GCC optimize("O3")
// #pragma GCC target("avx,avx2,fma")
#include <bits/stdc++.h>
#define FOR(i, a, b) for (int i = (a); i <= (b); i++)
#define FORD(i, a, b) for (int i = (a); i >= (b); i--)
#define REP(i, n) for (int i = 0; i < (n); i++)
#define ALL(x) (x).begin(), (x).end()
#define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
using namespace std;
const int MAXN = 3e5 + 5;
const long long INF = 1e18;
int n, m, ST, ED, U, V;
struct Edges{
int u, v, w;
} E[MAXN];
long long dist1[MAXN], dist2[MAXN];
vector <pair <int, int>> g[MAXN];
long long dist[MAXN];
signed main(){
ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
file("BUS");
cin >> n >> m >> ST >> ED >> U >> V;
FOR(i, 1, m){
cin >> E[i].u >> E[i].v >> E[i].w;
g[E[i].u].push_back(make_pair(E[i].v, E[i].w));
g[E[i].v].push_back(make_pair(E[i].u, E[i].w));
}
auto dijk = [&](int st, long long dist[]){
FOR(i, 1, n) dist[i] = INF;
#define pli pair <long long, int>
priority_queue <pli, vector <pli>, greater <pli>> pq;
pq.push({dist[st] = 0, st});
while(!pq.empty()){
int u = pq.top().second;
long long cost = pq.top().first;
pq.pop();
if(cost > dist[u]) continue;
for(const pair <int, int> &x : g[u]){
int v = x.first, w = x.second;
if(dist[v] > cost + w){
dist[v] = cost + w;
pq.push({dist[v], v});
}
}
}
};
dijk(ST, dist1);
dijk(ED, dist2);
auto dijkdag = [&](int st, int ed){
priority_queue <pli, vector <pli>, greater <pli>> pq;
vector <long long> dist(n + 2);
FOR(i, 1, n) dist[i] = INF;
pq.push({dist[st] = 0, st});
while(!pq.empty()){
int u = pq.top().second;
long long cost = pq.top().first;
pq.pop();
if(cost > dist[u]) continue;
for(auto x : g[u]){
int v = x.first, w = x.second;
w = (dist1[u] + w + dist2[v] == dist1[ED] ? 0 : w);
if(dist[v] > cost + w){
dist[v] = cost + w;
pq.push({dist[v], v});
}
}
}
return dist[ed];
};
cout << min(dijkdag(U, V), dijkdag(V, U));
return void(cerr << "\nKO: " << 0.001 * clock() << "s "), 0;
}
