//Coded by Chirath Nirodha
#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
using namespace std;
#define F first
#define S second
#define PB push_back
#define MP make_pair
#define P push
#define I insert
#define ER erase
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
typedef tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update> indexed_set;
const ll mod=1e9+7;
inline void io(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
}
int n,m,s,t,u,v;
vector<pair<ll,ll> > adj[100000];
vector<ll> dps,dpu,dpv,dpt;
vector<ll> su,sv,tu,tv;
vector<ll> dijkstra(int a){
vector<ll> dp;
for(int i=0;i<n;i++)dp.PB(INT64_MAX);
dp[a]=0;
priority_queue<pair<ll,ll> > q;
q.P(MP(0,a));
while(!q.empty()){
pair<ll,ll> c=q.top();q.pop();
for(int i=0;i<adj[c.S].size();i++){
ll x=adj[c.S][i].F,y=adj[c.S][i].S;
if(dp[x]>dp[c.S]+y){
dp[x]=dp[c.S]+y;
q.P(MP(-dp[x],x));
}
}
}
return dp;
}
ll ans;
void bfs(){
queue<int> q;
q.P(t);
tu[t]=dpu[t];tv[t]=dpv[t];
while(!q.empty()){
int c=q.front();q.pop();
for(int i=0;i<adj[c].size();i++){
ll x=adj[c][i].F,y=adj[c][i].S;
if(dps[x]+y!=dps[c])continue;
if(tu[x]>tu[c] || tv[x]>tv[c] || tu[x]>dpu[x] || tv[x]>dpv[x])q.P(x);
tu[x]=min(tu[x],min(tu[c],dpu[x]));
tv[x]=min(tv[x],min(tv[c],dpv[x]));
}
}
q.P(s);
su[s]=dpu[s];sv[s]=dpv[s];
while(!q.empty()){
int c=q.front();q.pop();
for(int i=0;i<adj[c].size();i++){
ll x=adj[c][i].F,y=adj[c][i].S;
if(dpt[x]+y!=dpt[c])continue;
if(su[x]>su[c] || sv[x]>sv[c] || su[x]>dpu[x] || sv[x]>dpv[x])q.P(x);
su[x]=min(su[x],min(su[c],dpu[x]));
sv[x]=min(sv[x],min(sv[c],dpv[x]));
}
}
}
void solve(){
cin>>n>>m>>s>>t>>u>>v;
s--;t--;u--;v--;
for(int i=0;i<m;i++){
ll x,y,z;cin>>x>>y>>z;x--;y--;
adj[x].PB(MP(y,z));adj[y].PB(MP(x,z));
}
dps=dijkstra(s);
dpt=dijkstra(t);
dpu=dijkstra(u);
dpv=dijkstra(v);
ans=dpu[v];
for(int i=0;i<n;i++){
su.PB(1000000000000);
sv.PB(1000000000000);
tu.PB(1000000000000);
tv.PB(1000000000000);
}
bfs();
for(int i=0;i<n;i++){
ans=min(ans,su[i]+tv[i]);
ans=min(ans,sv[i]+tu[i]);
}
cout<<ans<<endl;
}
int main(){
io();
solve();
//int t;cin>>t;for(int i=0;i<t;i++)solve();
return 0;
}
