//*
//#pragma GCC optimize("O2")
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("unroll-loops")
//#pragma GCC target("avx,avx2,sse,sse2,fma")
//*/
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define int ll
typedef long double ld;
typedef pair<int ,int > pii;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const ll maxn = 2e5 + 10;
const ll mod =1e9+7;
const ld PI = acos((ld)-1);
#define pb push_back
#define endl '\n'
#define dokme(x) cout << x , exit(0)
#define migmig ios::sync_with_stdio(false),cin.tie(0),cout.tie(0)
#define ms(x , y) memset(x , y , sizeof x)
ll pw(ll a, ll b, ll md = mod){ll res = 1;while(b){if(b&1){res=(a*res)%md;}a=(a*a)%md;b>>=1;}return(res);}
struct tr{
int u , w;
tr(int a , int b):
u(a) , w(b){}
friend bool operator < (tr a , tr b){
if(a.w == b.w)return(a.u < b.u);
return(a.w > b.w);
}
};
int n , m;
vector < tr > adj[maxn];
int s , t;
int a , b;
vector < int > ds , dt;
priority_queue < tr > st;
bool mark[maxn];
#define insert push
#define erase pop
void djk(int v, vector < int > &dist){
ms(mark , 0);
for(int i = 0 ; i <= n ; i ++)
dist.pb(1e18);
dist[v] = 0;
st.insert({v , dist[v]});
while(!st.empty()){
auto vw = (st.top());
auto v = vw.u;
st.erase();
if(mark[v])continue;
mark[v] = 1;
for(auto uw : adj[v])
if(dist[uw.u] > dist[v] + uw.w)
dist[uw.u] = dist[v] + uw.w,
st.insert({uw.u , dist[uw.u]});
}
}
vector < int > du , dv;
bool sp(int u , int v , int w){
return((ds[u] + dt[v] + w == ds[t]));
}
int mn[maxn] , mnr[maxn];
int ans = 1e18;
vector < int > in[maxn] , out[maxn];
int d[maxn];
vector < int > topo;
void dfs(int v){
topo.pb(v);
mark[v] = 1;
for(auto u : out[v]){
d[u] -- ;
if(d[u] == 0)
dfs(u);
}
}
int32_t main(){
migmig;
cin >> n >> m;
cin >> s >> t;
cin >> a >> b;
for(int i = 1; i <= m ; i ++){
int u , v , w;
cin >> u >> v >> w;
adj[u].pb({v , w});
adj[v].pb({u , w});
}
djk(s , ds);
djk(t , dt);
djk(a , du);
djk(b , dv);
for(int v = 1 ; v <= n ; v ++){
for(auto uw : adj[v]){
auto u = uw.u;
auto w = uw.w;
if(sp(v , u , w))in[u].pb(v) , out[v].pb(u) , d[u] ++ ;
}
}
ms(mark , 0);
for(int i = 1; i <= n ; i ++)if(d[i] == 0 and !mark[i])dfs(i);
for(int i = 1; i <= n ; i ++)mn[i] = 1e18 , mnr[i] = 1e18;
for(auto v : topo){
mn[v] = du[v];
for(auto u : in[v])
mn[v] = min(mn[v] , mn[u]);
}
reverse(topo.begin() , topo.end());
for(auto v : topo){
mnr[v] = du[v];
for(auto u : out[v])
mnr[v] = min(mnr[v] , mnr[u]);
}
for(int i = 1 ; i <= n ; i ++)mn[i] = min(mn[i] , mnr[i]);
for(int i = 1 ; i <= n ; i ++)
ans = min(ans , dv[i] + mn[i]);
cout << ans;
return(0);
}
