#include<bits/stdc++.h>
using namespace std;
typedef long long int lld;
typedef pair<lld,lld> pii;
#define rep(i,a,b) for(int i=a;i<b;i++)
#define trav(a,v) for(auto a:v)
#define INF 10000000000000000
int n,m,s,t,u,v;
vector<pii> nei[1000000];
vector<int> tree[1000000];
lld dist[1000000];
priority_queue<pii> pq;
void calc(int init){
rep(i,0,n)dist[i]=INF;
dist[init]=0;
pq.push(pii(0,init));
while(!pq.empty()){
int u=pq.top().second;
lld d=-pq.top().first;
pq.pop();
if(d>dist[u])continue;
//cout<<u<<" "<<d<<endl;
trav(V,nei[u]){
//cout<<v.first<<"A"<<v.second<<" "<<d<<" "<<dist[v.first]<<endl;
if(dist[V.first]>V.second+d){
dist[V.first]=V.second+d;
pq.push(pii(-dist[V.first],V.first));
}
}
}
}
bool visited[1000000];
void Rev(int node){
visited[node]=true;
trav(V,nei[node]){
if(dist[V.first]+V.second==dist[node]){
tree[node].push_back(V.first);
if(!visited[V.first])Rev(V.first);
}
}
}
lld dist_u[1000000];
lld dist_v[1000000];
lld min_dist_u[1000000];
lld min_dist_v[1000000];
lld calc_u(int node){
if(min_dist_u[node]!=-1)return min_dist_u[node];
min_dist_u[node]=dist_u[node];
trav(V,tree[node]){
min_dist_u[node]=min(min_dist_u[node],calc_u(V));
}
return min_dist_u[node];
}
lld calc_v(int node){
if(min_dist_v[node]!=-1)return min_dist_v[node];
min_dist_v[node]=dist_v[node];
trav(V,tree[node]){
min_dist_v[node]=min(min_dist_v[node],calc_v(V));
}
return min_dist_v[node];
}
int main(){
scanf("%d %d",&n,&m);
scanf("%d %d",&s,&t);
s--;t--;
scanf("%d %d",&u,&v);
u--;v--;
rep(i,0,m){
int x,y;
lld c;
scanf("%d %d %lld",&x,&y,&c);
x--;y--;
nei[x].push_back(pii(y,c));
nei[y].push_back(pii(x,c));
}
calc(s);
//rep(i,0,n)cout<<dist[i]<<endl;
rep(i,0,n){
visited[i]=false;
}
Rev(t);
/*rep(i,0,n){
trav(v,tree[i])cout<<v<<" ";
cout<<endl;
}*/
calc(u);
rep(i,0,n){
dist_u[i]=dist[i];
min_dist_u[i]=-1;
}
calc(v);
rep(i,0,n){
dist_v[i]=dist[i];
min_dist_v[i]=-1;
}
lld ans=dist_u[v];
rep(i,0,n){
if(visited[i]){
calc_u(i);
calc_v(i);
ans=min(ans,dist_v[i]+min_dist_u[i]);
ans=min(ans,dist_u[i]+min_dist_v[i]);
}
}
printf("%lld\n",ans);
return 0;
}
