#include <bits/stdc++.h>
using namespace std;
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
//#pragma GCC optimize("Ofast,unroll-loops,fast-math,O3")
#define pb push_back
#define ll long long
#define int long long
//#define sort(all(v)) sort(v.begin(),v.end())
int mod = 998244353;
const int N = 1e5 + 10;
const int inf = 1e9;
int fact[200001];
ll binpow(ll a, ll b){
if(b == 0) return 1;
else if(b % 2 == 1) return (a * binpow(a, b - 1)) % mod;
ll p = binpow(a,b / 2);
return (p * p) % mod;
}
map <pair<int,int>,bool> mp;
vector <pair<int,int>> g[N],g1[N];
signed main(){
//freopen("mootube.in", "r", stdin);
//freopen("mootube.out", "w", stdout);
int n,m;
cin >> n >> m;
int s,t;
cin >> s >> t;
int u,v;
cin >> u >> v;
vector <array<int,3>> q1;
for(int i = 1; i <= m; i++){
int a,b,c;
cin >> a >> b >> c;
g[a].pb({b,c});
g[b].pb({a,c});
q1.pb({a,b,c});
}
vector <int> d(n + 1,1e18),p(n + 1);
set <pair<int,int>> st;
st.insert({0,s});
d[s] = 0;
while(st.size() > 0){
int u1 = (*st.begin()).second;
st.erase(st.begin());
for(auto [to,w] : g[u1]){
if(d[to] > d[u1] + w){
st.erase({d[to],to});
d[to] = d[u1] + w;
p[to] = u1;
st.insert({d[to],to});
}
}
}
queue <int> q;
vector <int> bag;
q.push(t);
bag.pb(t);
while(!q.empty()){
int u = q.front();
q.pop();
if(p[u] != 0){
q.push(p[u]);
bag.pb(p[u]);
}
}
reverse(bag.begin(),bag.end());
for(int i = 0; i < bag.size() - 1; i++){
mp[{bag[i],bag[i + 1]}] = 1;
}
for(int i = 0; i < n; i++){
int a = q1[i][0],b = q1[i][1],c = q1[i][2];
if(mp[{a,b}] != 1){
g1[a].pb({b,c});
g1[b].pb({a,c});
}
else{
g1[a].pb({b,0ll});
g1[b].pb({a,0ll});
}
}
for(int i = 1; i <= n; i++) d[i] = 1e18;
st.insert({0,u});
d[u] = 0;
while(st.size() > 0){
int u1 = (*st.begin()).second;
st.erase(st.begin());
for(auto [to,w] : g1[u1]){
if(d[to] > d[u1] + w){
st.erase({d[to],to});
d[to] = d[u1] + w;
st.insert({d[to],to});
}
}
}
cout << d[v];
}
