#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define db double
#define ii pair<int,int>
#define f first
#define s second
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define ALL(v) v.begin(),v.end()
#define BIT(i) ((ll)1<<i)
#define endl "\n"
#define debug(x) for (auto p: x) cout<<p<<' ';cout<<endl
#define forw(i,j,z) for(int i=(int)j;i<=(int)z;i++)
#define forw2(i,j,z,k) for(int i=(int)j;i<=(int)z;i+=k)
#define ford(i,j,z) for (int i=(int)j;i>=(int)z;i--)
#define ford2(i,j,z,k) for (int i=(int)j;i>=(int)z;i-=k)
#define sz(a) (int)a.size()
const ll inf=BIT(60);
const int N=100000;
int n,m,s;
struct Edge{
int nex;ll cost;
Edge(int v1,ll d1)
{
nex=v1,cost=d1;
}
};
vector<Edge> a[N+1];
vector<ll> S,U,V,dpU,dpV;
vector<vector<int> > traceS;
ll ans;
bitset<N+1> vis;
void dijkstra(int S,vector<ll> &dp,bool TRACE)
{
dp.assign(n+1,LLONG_MAX);
dp[S]=0;
priority_queue<pair<ll,int>,vector<pair<ll,int> >,greater<pair<ll,int> > > haha;
haha.push(mp(0LL,S));
while(!haha.empty())
{
pair<ll,int> temp = haha.top();
haha.pop();
int u=temp.s;
if (temp.f>dp[u]) continue;
forw(i,0,sz(a[u])-1)
{
int v=a[u][i].nex,d=a[u][i].cost;
if (dp[u]+d<dp[v])
{
if (TRACE)
{
traceS[v].clear();
traceS[v].pb(u);
}
dp[v]=dp[u]+d;
haha.push(mp(dp[v],v));
}
else if (TRACE&&dp[u]+d==dp[v])
traceS[v].pb(u);
}
}
}
void dfs(int u)
{
vis[u]=1;
if (u==s)
{
dpU[u]=U[s],dpV[u]=V[s];
ans=min(ans,dpU[u]+dpV[u]);
return ;
}
dpU[u]=U[u],dpV[u]=V[u];
forw(i,0,sz(traceS[u])-1)
{
int v=traceS[u][i];
if (!vis[v]) dfs(v);
dpU[u]=min(dpU[u],dpU[v]);
dpV[u]=min(dpV[u],dpV[v]);
}
ans=min(ans,min(dpU[u]+V[u],dpV[u]+U[u]));
}
void solve()
{
int u,v,t;
cin>>n>>m;
cin>>s>>t>>u>>v;
traceS.assign(n+1,vector<int>(0,0));
dpU.assign(n+1,0);
dpV.assign(n+1,0);
while(m--)
{
int u,v;ll d;
cin>>u>>v>>d;
a[u].pb(Edge(v,d));
a[v].pb(Edge(u,d));
}
dijkstra(s,S,1);
dijkstra(u,U,0);
dijkstra(v,V,0);
ans=U[v];
dfs(t);
cout<<ans;
}
signed main()
{
ios_base::sync_with_stdio(false);
cin.tie(0);
cout<<setprecision(6)<<fixed;
int t=1;
while(t--)
solve();
return 0;
}
