#pragma GCC optimzize("Ofast,no-stack-protector")
#include<bits/stdc++.h>
#define int long long
#define quick ios::sync_with_stdio(0);cin.tie(0);
#define rep(x,a,b) for(int x=a;x<=b;x++)
#define repd(x,a,b) for(int x=a;x>=b;x--)
#define lowbit(x) (x&-x)
#define sz(x) (int)(x.size())
#define F first
#define S second
#define all(x) x.begin(),x.end()
#define mp make_pair
#define eb emplace_back
using namespace std;
typedef complex<int> P;
#define X real()
#define Y imag()
typedef pair<int,int> pii;
void debug(){
cout<<"\n";
}
template <class T,class ... U >
void debug(T a, U ... b){
cout<<a<<" ",debug(b...);
}
const int N=2e5+7;
const int INF=1e18;
int dis[N];
int dis2[N];
int dis3[N];
vector<pii> v[N];
vector<pii> v2[N];
int uf[N];
int ut[N];
signed main(){
quick
int n,m;
int s,e,f,t;
cin>>n>>m;
cin>>s>>e>>f>>t;
rep(i,1,m){
int a,b,c;
cin>>a>>b>>c;
v[a].eb(mp(c,b));
v[b].eb(mp(c,a));
}
fill(dis,dis+N,INF);
fill(dis2,dis2+N,INF);
dis[f]=0;
priority_queue<pii,vector<pii> ,greater<pii> > pq;
pq.push(mp(0,f));
while(sz(pq)){
pii now=pq.top();
pq.pop();
if(dis[now.S]<now.F) continue;
for(pii p2:v[now.S]){
if(dis[p2.S]>dis[now.S]+p2.F){
pq.push(mp(dis[p2.S]=dis[now.S]+p2.F,p2.S));
}
}
}
dis2[t]=0;
pq.push(mp(0,t));
while(sz(pq)){
pii now=pq.top();
pq.pop();
if(dis2[now.S]<now.F) continue;
for(pii p2:v[now.S]){
if(dis2[p2.S]>dis2[now.S]+p2.F){
pq.push(mp(dis2[p2.S]=dis2[now.S]+p2.F,p2.S));
}
}
}
rep(i,1,n){
uf[i]=ut[i]=-1;
}
fill(dis3,dis3+N,INF);
pq.push(mp(0,s));
dis3[s]=0;
uf[s]=ut[s]=s;
while(sz(pq)){
pii now=pq.top();
pq.pop();
if(dis3[now.S]<now.F) continue;
for(pii p2:v[now.S]){
if(dis3[p2.S]>dis3[now.S]+p2.F){
if(dis[p2.S]<dis[uf[now.S]]) uf[p2.S]=p2.S;
else uf[p2.S]=uf[now.S];
if(dis2[p2.S]<dis2[ut[now.S]]) ut[p2.S]=p2.S;
else ut[p2.S]=ut[now.S];
pq.push(mp(dis3[p2.S]=dis3[now.S]+p2.F,p2.S));
}
else if(dis3[p2.S]==dis3[now.S]+p2.F){
int p=(dis[uf[now.S]] > dis[p2.S] ? p2.S : uf[now.S]);
int q=(dis2[ut[now.S]] > dis2[p2.S] ? p2.S :ut[now.S]);
if(dis[uf[p2.S]]+dis2[ut[p2.S]]>dis[p]+dis2[q]){
uf[p2.S]=p;
ut[p2.S]=q;
}
}
}
}
/*debug("dis",f,":");rep(i,1,n) cout<<dis[i]<<" \n"[i==n];
debug("dis2",t,":");rep(i,1,n) cout<<dis2[i]<<" \n"[i==n];
debug("dis3",s,":");rep(i,1,n) cout<<dis3[i]<<" \n"[i==n];
debug("uf");rep(i,1,n) cout<<uf[i]<<" \n"[i==n];
debug("ut");rep(i,1,n) cout<<ut[i]<<" \n"[i==n];
*/
cout<<min(dis[uf[e]]+dis2[ut[e]],dis[t])<<"\n";
return 0;
}
