#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pi;
typedef vector <ll> vi;
typedef vector <pi> vpi;
#define f first
#define s second
#define FOR(i,s,e) for(ll i=s;i<=ll(e);++i)
#define DEC(i,s,e) for(ll i=s;i>=ll(e);--i)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define lbd(x, y) lower_bound(all(x), y)
#define ubd(x, y) upper_bound(all(x), y)
#define aFOR(i,x) for (auto i: x)
#define mem(x,i) memset(x,i,sizeof x)
#define fast ios_base::sync_with_stdio(false),cin.tie(0)
#define maxn 200001
#define INF 1e10
#define int ll
typedef pair <pi,int> pii;
int N,M,S,T,U,V;
int distS[maxn],distV[maxn], distU[maxn],distT[maxn];
vpi adj[maxn];
vi dag[maxn];
int dp[maxn];
int minE[maxn];
int minS[maxn];
int dpf(int x){
if (dp[x] != -1) return dp[x];
dp[x] = INF;
int E = INF;
int mnS = INF;
aFOR(i,dag[x]){
E = min(E,minE[x]);
mnS = min(mnS,minS[x]);
dp[x] = min(dp[x],dpf(i));
}
dp[x] = min(dp[x],distU[x] + E);
dp[x] = min(dp[x],distV[x] + mnS);
dp[x] = min(dp[x],distU[x] + distV[x]);
return dp[x];
}
int dfs(int x){ //to find minE
minE[x] = distV[x];
minS[x] = distU[x];
aFOR(i,dag[x]){
dfs(i);
minE[x] = min(minE[x],minE[i]);
minS[x] = min(minS[x],minS[i]);
}
return minE[x];
}
int32_t main(){
fast;
cin>>N>>M>>S>>T>>U>>V;
vector <pii> edges;
FOR(i,0,M-1){
int a,b,c; cin>>a>>b>>c;
adj[a].pb(pi(b,c)); adj[b].pb(pi(a,c));
edges.pb(pii(pi(a,b),c));
}
int rt = S;
priority_queue <pi> pq;
mem(distS,-1);
distS[rt] = 0;
pq.push(pi(0,rt));
while (!pq.empty()){
pi cur = pq.top(); pq.pop();
if (distS[cur.s] != cur.f) continue;
aFOR(i,adj[cur.s]){
if (distS[i.f] == -1 || distS[i.f] > cur.f + i.s){
distS[i.f] = cur.f + i.s;
pq.push(pi(distS[i.f],i.f));
}
}
}
rt = T;
mem(distT,-1);
distT[rt] = 0;
pq.push(pi(0,rt));
while (!pq.empty()){
pi cur = pq.top(); pq.pop();
if (distT[cur.s] != cur.f) continue;
aFOR(i,adj[cur.s]){
if (distT[i.f] == -1 || distT[i.f] > cur.f + i.s){
distT[i.f] = cur.f + i.s;
pq.push(pi(distT[i.f],i.f));
}
}
}
rt = U;
mem(distU,-1);
distU[rt] = 0;
pq.push(pi(0,rt));
while (!pq.empty()){
pi cur = pq.top(); pq.pop();
if (distU[cur.s] != cur.f) continue;
aFOR(i,adj[cur.s]){
if (distU[i.f] == -1 || distU[i.f] > cur.f + i.s){
distU[i.f] = cur.f + i.s;
pq.push(pi(distU[i.f],i.f));
}
}
}
rt = V;
mem(distV,-1);
distV[rt] = 0;
pq.push(pi(0,rt));
while (!pq.empty()){
pi cur = pq.top(); pq.pop();
if (distV[cur.s] != cur.f) continue;
aFOR(i,adj[cur.s]){
if (distV[i.f] == -1 || distV[i.f] > cur.f + i.s){
distV[i.f] = cur.f + i.s;
pq.push(pi(distV[i.f],i.f));
}
}
}
return 0;
aFOR(i,edges){
int a = i.f.f, b = i.f.s, c = i.s;
if (distS[a] + c + distT[b] == distS[T]){
dag[a].pb(b);
//cout<<a<<' '<<b<<'\n';
}else if(distS[b] + c + distT[a] == distS[T]){
dag[b].pb(a);
//cout<<b<<' '<<a<<'\n';
}
}
dfs(S);
mem(dp,-1);
int ans = min(distU[V],dpf(S));
cout<<ans;
}
