#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5+10;
#define f first
#define s second
typedef long long ll;
typedef pair<ll,ll> pii;
typedef pair<ll,pii> pip;
const ll inf = 1e18;
int n, m, a, b, s, t;
ll d[4][maxn], dp[2][maxn]; // 0 = a, 1 = b, 2 = s, 3 = t
vector<pii> grafo[maxn];
void dijkstra(int id, int root){
if(id <=1){
priority_queue<pii, vector<pii>, greater<pii>> fila;
fila.push({0, root});
while(!fila.empty()){
ll u = fila.top().s, dist = fila.top().f;
fila.pop();
if(d[id][u] != -1) continue;
d[id][u] = dist;
for(auto vv : grafo[u]){
int v = vv.s, w = vv.f;
if(d[id][v] == -1) fila.push({dist + w, v});
}
}
}
else{
priority_queue<pip, vector<pip>, greater<pip>> fila;
fila.push({0, {root, d[1][root]}});
while(!fila.empty()){
ll u = fila.top().s.f, dist = fila.top().f, tfg = fila.top().s.s;
fila.pop();
if(d[id][u] != -1){
if(d[id][u] == dist) dp[id-2][u] = min(dp[id-2][u], tfg);
continue;
}
d[id][u] = dist;
dp[id-2][u] = min(dp[id-2][u], tfg);
for(auto vv : grafo[u]){
int v = vv.s, w = vv.f;
if(d[id][v] == -1) fila.push({dist + w, {v, min(dp[id-2][u], d[1][v])}});
}
}
}
}
int main(){
ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
cin >> n >> m >> s >> t >> a >> b;
for(int i=1; i<=m; i++){
int u, v, w;
cin >> u >> v >> w;
grafo[u].push_back({w, v});
grafo[v].push_back({w, u});
}
memset(d, -1, sizeof d);
for(int i=1; i<=n; i++) dp[0][i] = dp[1][i] = inf;
dijkstra(0, a), dijkstra(1, b), dijkstra(2, s), dijkstra(3, t);
ll ans = inf;
for(int i=1; i<=n; i++){
ans = min(ans, d[0][i] + d[1][i]);
if(d[2][i] + d[3][i] == d[2][t]){
ans = min(ans, d[0][i] + min(dp[0][i], dp[1][i]));
}
}
cout << ans << "\n";
return 0;
}
