#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];
vector<pii> v[N];
int in[N];
vector<pii> v2[N];
vector<int> From[N];
int D[301][301];
int p[N];
int sz[N];
void init(int n){
rep(i,1,n){
p[i]=i,sz[i]=1;
}
}
int fp(int x){
if(x!=p[x]) p[x]=fp(p[x]);
return p[x];
}
void Union(int a,int b){
a=fp(a);b=fp(b);
if(a==b) return ;
if(sz[a]<sz[b]) swap(a,b);
sz[a]+=sz[b];
p[b]=a;
}
vector<int> vec;
int s,e,f,t,n;
int ans=INF;
void solve(){
vector<tuple<int,int,int> > rev;
for(int i:vec){
rev.eb(make_tuple(s,i,D[s][i]));
rev.eb(make_tuple(e,i,D[e][i]));
D[s][i]=D[i][s]=0;
D[e][i]=D[e][i]=0;
}
fill(dis,dis+n+1,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;
rep(i,1,n){
if(dis[i]>dis[now.S]+D[i][now.S]){
pq.push(mp(dis[i]=dis[now.S]+D[i][now.S],i));
}
}
}
ans=min(ans,dis[t]);
for(auto[a,b,c]:rev){
D[a][b]=D[b][a]=c;
}
}
bool invec[N];
void dfs(int now){
if(invec[now]) return ;
vec.eb(now);
invec[now]=true;
if(now==s){
solve();
vec.pop_back();
invec[s]=false;
return ;
}
for(int i=0;i<sz(From[now]);i++){
dfs(From[now][i]);
}
invec[now]=false;
vec.pop_back();
}
signed main(){
quick
int m;
cin>>n>>m;
cin>>s>>e>>f>>t;
if(n<=300){
rep(i,1,n){
rep(j,1,n) D[i][j]=INF;
}
}
rep(i,1,m){
int a,b,c;
cin>>a>>b>>c;
v[a].eb(mp(c,b));
v[b].eb(mp(c,a));
if(n<=300){
D[a][b]=D[b][a]=min(D[a][b],c);
}
}
fill(dis,dis+N,INF);
fill(dis2,dis2+N,INF);
dis[s]=0;
priority_queue<pii,vector<pii> ,greater<pii> > pq;
pq.push(mp(0,s));
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));
}
if(n<=300&&dis[p2.S]==dis[now.S]+p2.F){
From[p2.S].eb(now.S);
}
}
}
dis2[e]=0;
pq.push(mp(0,e));
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));
}
}
}
if(n<=300){
dfs(e);
cout<<ans<<"\n";
return 0;
}
init(n);
Union(s,e);
rep(i,1,n){
if(dis[i]+dis2[i]==dis[e]){
Union(i,e);
v[s].eb(mp(0,i));
v[i].eb(mp(0,s));
v[e].eb(mp(0,i));
v[i].eb(mp(0,e));
}
}
fill(dis,dis+N,INF);
dis[f]=0;
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));
}
}
}
cout<<dis[t]<<"\n";
return 0;
}
