#include "bits/stdc++.h"
#define MAXN 100009
#define INF 1000000007
#define mp(x,y) make_pair(x,y)
#define all(v) v.begin(),v.end()
#define pb(x) push_back(x)
#define wr cout<<"----------------"<<endl;
#define ppb() pop_back()
#define tr(ii,c) for(__typeof((c).begin()) ii=(c).begin();ii!=(c).end();ii++)
#define ff first
#define ss second
#define my_little_dodge 46
#define debug(x) cerr<< #x <<" = "<< x<<endl;
using namespace std;
typedef long long ll;
typedef pair<int,int> PII;
template<class T>bool umin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
template<class T>bool umax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
int n,m,u,v,s,t;
vector<PII>adj[MAXN];
const ll B=1e15;
ll dis[MAXN],d1[MAXN],d2[MAXN],dp[MAXN];
ll dp1[MAXN],dp2[MAXN],d3[MAXN],d4[MAXN];
void bfs(int st){
for(int i=1;i<=n;i++)
dis[i]=B;
priority_queue<PII,vector<PII>,greater<PII> >q;
q.push(mp(0,st));dis[st]=0;
while(!q.empty()){
int nd=q.top().ss;q.pop();
tr(it,adj[nd])
if(umin(dis[it->ff],dis[nd]+it->ss))
q.push(mp(dis[it->ff],it->ff));
}
}
void kfs(int st){
for(int i=1;i<=n;i++)
dis[i]=B,dp[i]=B;
priority_queue<PII,vector<PII>,greater<PII> >q;
q.push(mp(0,st));dis[st]=0;dp[st]=d2[st];
while(!q.empty()){
int nd=q.top().ss;q.pop();
tr(it,adj[nd])
if(dis[it->ff]>dis[nd]+it->ss){
dis[it->ff]=dis[nd]+it->ss;
q.push(mp(dis[it->ff],it->ff));
dp[it->ff]=min(dp[nd],d2[it->ff]);
}
else if(dis[it->ff]==dis[nd]+it->ss)
umin(dp[it->ff],min(dp[nd],d2[it->ff]));
}
}
int main(){
//~ freopen("file.in", "r", stdin);
scanf("%d%d%d%d%d%d",&n,&m,&s,&t,&u,&v);
while(m--){
int uu,vv,w;
scanf("%d%d%d",&uu,&vv,&w);
adj[uu].pb(mp(vv,w));
adj[vv].pb(mp(uu,w));
}
bfs(u);for(int i=1;i<=n;i++)d1[i]=dis[i];
bfs(v);for(int i=1;i<=n;i++)d2[i]=dis[i];
kfs(s);for(int i=1;i<=n;i++)d3[i]=dis[i],dp1[i]=dp[i];
kfs(t);for(int i=1;i<=n;i++)d4[i]=dis[i],dp2[i]=dp[i];
ll ans=d1[v];
for(int i=1;i<=n;i++)
if(d3[i]+d4[i]==d3[t])
umin(ans,d1[i]+min(dp1[i],dp2[i]));
printf("%lld\n",ans);
return 0;
}
