#include<iostream>
#include<stack>
#include<map>
#include<vector>
#include<string>
#include<unordered_map>
#include <queue>
#include<cstring>
#include<limits.h>
#include<cmath>
#include<set>
#include<algorithm>
#include<bitset>
using namespace std;
#define ll long long
#define f first
#define endl "\n"
#define s second
#define pii pair<int,int>
#define ppii pair<pii,pii>
#define pb push_back
#define p push
#define fastio ios::sync_with_stdio(false);cin.tie(NULL);
using namespace std;
const int mxn=1e5;
int n,m,s,t,u,v;
#define int long long
vector<pii>adj[mxn+10];
bitset<mxn+10>vis;
struct dat{
ll dv,du,c,d;
bool operator<(const dat&a)const{
if(c==a.c)return (dv+du)<(a.dv+du);
return d<a.d;
}
};
void dijk(int st,vector<int>&dist){
priority_queue<pii,vector<pii>,greater<pii>>pq;
pq.p({0,st});
dist[st]=0;
while(!pq.empty()){
int cur=pq.top().s;
pq.pop();
if(vis[cur])continue;
vis[cur]=true;
for(auto i:adj[cur]){
if(dist[i.f]==-1||dist[i.f]>dist[cur]+i.s){
dist[i.f]=dist[cur]+i.s,pq.p({dist[i.f],i.f});
}
}
}
vis.reset();
}
int32_t main(){
fastio
cin>>n>>m>>s>>t>>u>>v;
while(m--){
int a,b,c;cin>>a>>b>>c;
adj[a].pb({b,c});
adj[b].pb({a,c});
}
vector<int>dist1(n+1,-1);
vector<int>dist2(n+1,-1);
dijk(u,dist1);
dijk(v,dist2);
priority_queue<dat>pq;
pq.p({dist2[s],dist1[s],s,0});
vector<pair<int,pii>>dist(n+1,{-1,{-1,-1}});
dist[s]={0,{dist2[s],dist1[s]}};
while(!pq.empty()){
dat cur=pq.top();
pq.pop();
if(vis[cur.c])continue;
vis[cur.c]=true;
for(auto i:adj[cur.c]){
if(dist[i.f].f==-1||dist[i.f].f>dist[cur.c].f+i.s){
int ndu=min(cur.du,dist1[i.f]),ndv=min(cur.dv,dist2[i.f]);
dist[i.f]={dist[cur.c].f+i.s,{ndu,ndv}};
pq.p({ndv,ndu,i.f,dist[i.f].f});
}
}
}
cout<<min(dist[t].s.f+dist[t].s.s,dist1[v]);
}
