#define here cerr<<"===========================================\n"
#include <bits/stdc++.h>
#define ld double
#define ll long long
#define llinf 100000000000000000LL // 10^17
#define pb push_back
#define popb pop_back
#define fi first
#define sc second
#define endl '\n'
#define pll pair<ll,ll>
#define pld pair<ld,ld>
#define sz(a) (ll)(a.size())
#define all(a) a.begin(),a.end()
#define ceri(a,l,r) {for(ll i_ = l;i_<=r;i_++) cerr<<a[i_]<< " ";cerr<<endl;}
#define daj_mi_malo_vremena ios_base::sync_with_stdio(false);cerr.tie(0);cout.tie(0);cin.tie(0);
using namespace std;
#define maxn 100005
ll n,m;
vector<pll> g[maxn];
vector<ll> dg[maxn];
ll s,t,u,v;
ll d1[maxn];
ll d2[maxn];
ll dpu[maxn];
ll dpv[maxn];
ll dp[maxn];
bool vis[maxn];
vector<ll> b;
void dis(ll* d,ll c){
fill(d,d+n+1,llinf);
d[c] = 0;
priority_queue<pll> q;
q.push({0,c});
vector<bool> vis(n+1);
while(sz(q)){
ll u = q.top().sc;
q.pop();
if(vis[u]) continue;
vis[u] = 1;
for(pll p : g[u]){
ll s = p.fi;
ll w = p.sc;
if(d[u]+w<d[s]){
d[s] = d[u] + w;
q.push({-d[s],s});
}
}
}
//cerr<<"source: "<<c<<endl;
//ceri(d,1,n);
}
void top(ll u){
vis[u] = 1;
for(ll s : dg[u]){
if(vis[s]) continue;
top(s);
}
b.pb(u);
}
int main(){
daj_mi_malo_vremena
cin >> n >> m >> s >> t >> u >> v;
for(ll i = 1;i<=m;i++){
ll x,y,w; cin >> x >> y >> w;
g[x].pb({y,w});
g[y].pb({x,w});
}
dis(d1,s);
dis(d2,t);
for(ll i = 1;i<=n;i++){
for(pll p : g[i]){
ll j = p.fi;
ll w = p.sc;
if(d1[i] + w + d2[j]==d1[t]){
dg[i].pb(j);
}
}
}
top(s);
dis(d1,u);
dis(d2,v);
fill(dp,dp+n+1,llinf);
fill(dpv,dpv+n+1,llinf);
fill(dpu,dpu+n+1,llinf);
for(ll x : b){
dp[x] = d1[x] + d2[x];
dpu[x] = d1[x];
dpv[x] = d2[x];
for(pll p : g[x]){
ll y = p.fi;
ll w = p.sc;
dpu[x] = min(dpu[x],dpu[y]);
dpv[x] = min(dpv[x],dpv[y]);
dp[x] = min(dp[x],dp[y]);
}
dp[x] = min({dp[x],dpu[x]+d2[x],d1[x]+dpv[x]});
}
cout<<min(dp[s],d1[v])<<endl;
return 0;
}
/*
6 6
1 6
1 4
1 2 1
2 3 1
3 5 1
2 4 3
4 5 2
5 6 1
*/
