#include<bits/stdc++.h>
#define mp make_pair
#define pb push_back
#define ii pair<int,int>
#define all(x) (x).begin(),(x).end()
#define INF 100000000000000000
#define modulo 1000000007
#define mod 998244353
#define int long long int
using namespace std;
vector<ii>adj[100005];
struct Shortest_path{
vector<int>val;
int start;
Shortest_path(){}
Shortest_path(int n,int s){
start=s;
val.resize(n,INF);
val[s]=0;
vector<bool>vis(n,false);
priority_queue<ii,vector<ii>,greater<ii>>Q;
Q.push({0,s});
while(!Q.empty()){
int x=Q.top().second;Q.pop();
if(vis[x])continue;
vis[x]=true;
for(int i=0;i<adj[x].size();i++){
int y=adj[x][i].first,z=adj[x][i].second;
if(vis[y]||val[y]<=val[x]+z)continue;
val[y]=val[x]+z;
Q.push({val[y],y});
}
}
}
};
Shortest_path comm;
Shortest_path data1;
Shortest_path data2;
vector<int> path[100005];
vector<int> indeg(100005,0);
vector<ii>dp[100005];
int ans=INF;
void merge(vector<ii>& A,vector<ii>& B){
vector<ii>C;
int ind=0;
for(int i=0;i<A.size();i++){
while(ind<B.size()&&B[ind].first<=A[i].first){
if(C.empty()||B[ind].second<C.back().second)C.pb(B[ind]);
ind++;
}
if(C.empty()||A[i].second<C.back().second)C.pb(A[i]);
}
while(ind<B.size()){
if(C.empty()||B[ind].second<C.back().second)C.pb(B[ind]);
ind++;
}
swap(B,C);
}
void dfs(int x){
for(int i=0;i<dp[x].size();i++){
dp[x][i].first=min(dp[x][i].first,data1.val[x]);
dp[x][i].second=min(dp[x][i].second,data2.val[x]);
ans=min(ans,dp[x][i].first+dp[x][i].second);
}
for(int i=0;i<path[x].size();i++){
int y=path[x][i];
indeg[y]--;
merge(dp[x],dp[y]);
dp[x].clear();
if(indeg[y]==0)dfs(y);
}
}
int32_t main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
// freopen("q.gir","r",stdin);
// freopen("q.cik","w",stdout);
int n,m,S,T,U,V;
cin>>n>>m>>S>>T>>U>>V;swap(S,T);
for(int i=0;i<m;i++){
int a,b,c;
cin>>a>>b>>c;
adj[a].pb({b,c});
adj[b].pb({a,c});
}
comm=Shortest_path(n+1,S);
data1=Shortest_path(n+1,U);
data2=Shortest_path(n+1,V);
ans=data1.val[V];
queue<int>Q;
vector<bool>vis(n+1,false);
Q.push(T);
while(!Q.empty()){
int x=Q.front();
Q.pop();
if(vis[x])continue;
vis[x]=true;
for(int i=0;i<adj[x].size();i++){
int y=adj[x][i].first,z=adj[x][i].second;
if(comm.val[x]==comm.val[y]+z){
Q.push(y);
path[x].pb(y);
indeg[y]++;
}
}
}
dp[T].pb({INF,INF});
dfs(T);
cout<<ans;
}
