#include <bits/stdc++.h>
using namespace std;
#define forw(i,a,b) for(int i=a;i<=b;i++)
#define forb(i,a,b) for(int i=a;i>=b;i--)
#define pu push
#define pb push_back
#define fi first
#define se second
#define all(a) a.begin(),a.end()
typedef long long int ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef pair<ll,pair<ll,ll> > plll;
const ll maxN=2e5+5;
const ll oo=1e18;
ll n,m,s,t,u,v,d[305][305],dist[maxN][5],way[maxN][5];
vector <plll> save;
vector <pll> edge[maxN];
void dijk(int s, int id)
{
forw(i,1,n) dist[i][id]=oo;
dist[s][id]=0;
way[s][id]=1;
priority_queue<pll,vector <pll> , greater<pll> > p;
p.pu({0,s});
while (p.size())
{
ll val=p.top().fi;
ll u=p.top().se;
p.pop();
if (val>dist[u][id]) continue;
for(auto tmp:edge[u])
{
ll v=tmp.se; ll add=tmp.fi;
if (val+add<dist[v][id])
{
way[v][id]=way[u][id];
dist[v][id]=val+add;
p.pu({dist[v][id],v});
}
else
if (val+add==dist[v][id]) way[v][id]+=way[u][id];
}
}
return;
}
void init()
{
forw(i,1,m)
{
ll u,v,z;
z=save[i-1].fi; u=save[i-1].se.fi; v=save[i-1].se.se;
edge[u].pb({z,v});
edge[v].pb({z,u});
}
dijk(s,0);
dijk(t,1);
return;
}
void sub1()
{
//cout<<"subtask 1\n";
dijk(v,2);
ll ans=dist[u][2];
forw(i,1,n)
if (dist[i][0]+dist[i][1]==dist[t][0])
ans=min(ans,dist[i][2]);
cout<<ans;
return;
}
void sub2()
{
//cout<<"subtask 2\n";
for(auto tmp:save)
{
ll u=tmp.se.fi;
ll v=tmp.se.se;
ll val=tmp.fi;
if (dist[u][0]+val+dist[v][1]==dist[t][0] || dist[u][1]+val+dist[v][0]==dist[t][0])
{
edge[u].pb({0,v});
edge[v].pb({0,u});
}
}
dijk(u,2);
cout<<dist[v][2];
return;
}
void sub3()
{
//cout<<"subtask 3\n";
forw(i,1,n)
forw(j,1,n)
if (i!=j) d[i][j]=oo;
forw(i,1,m)
{
ll u,v,z;
z=save[i-1].fi; u=save[i-1].se.fi; v=save[i-1].se.se;
d[u][v]=d[v][u]=min(d[u][v],z);
}
forw(k,1,n)
forw(i,1,n)
forw(j,1,n)
d[i][j]=min(d[i][j],d[i][k]+d[k][j]);
vector <pii> pend;
forw(i,1,n)
forw(j,1,n)
if (d[s][i]+d[i][j]+d[j][t]==d[s][t])
pend.pb({i,j});
for(auto tmp:pend)
d[tmp.fi][tmp.se]=d[tmp.se][tmp.fi]=0;
ll ans=d[u][v];
forw(i,1,n)
forw(j,1,n)
ans=min(ans,d[u][i]+d[i][j]+d[j][v]);
cout<<ans;
return;
}
int main()
{
ios::sync_with_stdio();
cin.tie(0);
//freopen("b.inp","r",stdin);
//freopen("b.out","w",stdout);
cin>>n>>m;
cin>>s>>t;
cin>>u>>v;
forw(i,1,m)
{
ll u,v,z; cin>>u>>v>>z;
save.pb({z,{u,v}});
}
init();
if (s==u) sub1();
else
if (way[t][0]==1) sub2();
else sub3();
return 0;
}
