#include <bits/stdc++.h>
using namespace std;
#define int long long
#define in ({int x=0;int c=getchar(),n=0;for(;!isdigit(c);c=getchar()) n=(c=='-');for(;isdigit(c);c=getchar()) x=x*10+c-'0';n?-x:x;})
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int rnd(int l,int r){return l+rng()%(r-l+1);}
#define fasty ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0);
#define fori(x,a,b) for (int x=a;x<=b;x++)
#define ford(x,a,b) for (int x=a;x>=b;x--)
#define forv(a,b) for(auto&a:b)
#define fi first
#define se second
#define pb push_back
#define ii pair<int,int>
#define all(a) a.begin(),a.end()
#define reset(f, x) memset(f, x, sizeof(f))
#define getbit(x,i) ((x>>i)&1)
#define batbit(x,i) (x|(1ll<<i))
#define tatbit(x,i) (x&~(1<<i))
#define gg exit(0);
const int maxn = 2e5 + 10;
int n,m,s,t,x,y;
vector<ii> ke[maxn];
vector<int> dij(int s)
{
vector<int> f(n+5,1e15);
priority_queue<ii,vector<ii>,greater<ii> > h;
f[s] = 0;
h.push({0,s});
while(!h.empty())
{
ii u = h.top();
h.pop();
int umin = u.se,dmin = u.fi;
forv(v,ke[umin]) if(f[v.fi] > dmin + v.se)
{
f[v.fi] = dmin + v.se;
h.push({f[v.fi],v.fi});
}
}
return f;
}
void sub1()
{
vector<int> fs,ft,fy;
fs = dij(s);
ft = dij(t);
fy = dij(y);
int kq = 1e15;
fori(i,1,n) if(fs[i]+ft[i]==fs[t]) kq = min(kq,fy[i]);
cout<<kq;
}
vector<int> ad[maxn];
int dd[maxn],pre[maxn];
pair<ii,int> e[maxn];
void sub2()
{
vector<int> f(n+5,1e15);
priority_queue<ii,vector<ii>,greater<ii> > h;
f[s] = 0;
h.push({0,s});
while(!h.empty())
{
ii u = h.top();
h.pop();
int umin = u.se,dmin = u.fi;
forv(i,ad[umin])
{
int v = e[i].fi.fi;
if(v==umin) v = e[i].fi.se;
if(f[v] > dmin + e[i].se)
{
pre[v] = i;
f[v] = dmin + e[i].se;
h.push({f[v],v});
}
}
}
int ket = t;
while(pre[ket])
{
int i = pre[ket];
int v = e[i].fi.fi;
if(v==ket) v = e[i].fi.se;
ket = v;
dd[i] = 1;
}
fori(i,1,n) ke[i].clear();
fori(i,1,m)
{
int u = e[i].fi.fi,v = e[i].fi.se,c = e[i].se;
if(dd[i]) c = 0;
ke[u].pb({v,c}),ke[v].pb({u,c});
}
vector<int> fx = dij(x);
cout<<fx[y];
}
main()
{
//freopen("task.inp","r",stdin);
fasty;
cin>>n>>m;
cin>>s>>t>>x>>y;
fori(i,1,m)
{
int u,v,c;cin>>u>>v>>c;
ke[u].pb({v,c}),ke[v].pb({u,c});
ad[u].pb(i),ad[v].pb(i);
e[i] = {{u,v},c};
}
if(s==x) sub1();
else sub2();
}
/*
chon 1 dg di ngan nhat tu s->t,cho tat cac canh tren dg di nay = 0
sao cho dg di ngan nhat tu u->v la MIN
*/
//https://oj.uz/problem/view/JOI18_commuter_pass
