#include <bits/stdc++.h>
using namespace std;
#define endl '\n'
#define pll pair<long long, long long>
const int sz = 1e5 + 5;
vector<pll> gr[sz];
long long d[5][sz];
long long f[5][sz];
int n, m, S, T, U, V;
//constants
long long ST;
long long UV;
void Dijkstra(int k, int s){
priority_queue<pll> q;
d[k][s] = 0;
q.push({0, s});
while(q.size()){
long long w, u;
tie(w, u) = q.top();
w = -w;
q.pop();
if(w > d[k][u]){
continue;
}
for(pll p : gr[u]){
long long v, c;
tie(v, c) = p;
if(w + c < d[k][v]){
d[k][v] = w + c;
q.push({-d[k][v], v});
}
}
}
}
vector<int> dag[sz];
int vi[sz];
void build_DAG(int v){
vi[v] = 1;
for(pll p : gr[v]){
long long u, c;
tie(u, c) = p;
if(d[0][u] + c + d[1][v] == ST){
dag[u].push_back(v);
if(vi[u] == 0){
build_DAG(u);
}
}
}
}
deque<int> tp;
void topo(int u){
vi[u] = 2;
for(int v : dag[u]){
if(vi[v] != 2){
topo(v);
}
}
tp.push_front(u);
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
// freopen("main.inp","r",stdin);
// freopen("main.out","w",stdout);
cin >> n >> m;
cin >> S >> T;
cin >> U >> V;
while(m--){
int u, v, c;
cin>>u>>v>>c;
gr[u].push_back({v, c});
gr[v].push_back({u, c});
}
memset(d, 63, sizeof(d));
Dijkstra(0, S);
Dijkstra(1, T);
Dijkstra(2, U);
Dijkstra(3, V);
ST = d[0][T];
UV = d[2][V];
build_DAG(T);
topo(S);
for(int i=1;i<=n;++i){
f[0][i] = d[2][i]; // U -> i
f[1][i] = d[3][i]; // V -> i
}
for(int u : tp){
for(int v : dag[u]){
f[0][v] = min(f[0][v], f[0][u]);
f[1][v] = min(f[1][v], f[1][u]);
}
}
long long ans = UV;
for(int i=1;i<=n;++i){
if(d[0][i] + d[1][i] == ST){
ans = min({ans, f[0][i] + d[3][i], f[1][i] + d[2][i]});
}
}
cout<<ans;
return 0;
}
