#include<bits/stdc++.h>
#define ll long long int
#define pb push_back
#define mp make_pair
#define FOR(i,n) for(i=0;i<(n);++i)
#define FORe(i,n) for(i=1;i<=(n);++i)
#define FORr(i,a,b) for(i=(a);i<(b);++i)
#define FORrev(i,n) for(i=(n);i>=0;--i)
#define F0R(i,n) for(int i=0;i<(n);++i)
#define F0Re(i,n) for(int i=1;i<=(n);++i)
#define F0Rr(i,a,b) for(ll i=(a);i<(b);++i)
#define F0Rrev(i,n) for(int i=(n);i>=0;--i)
#define ii pair<ll,ll>
#define vi vector<ll>
#define vii vector<ii>
#define ff first
#define ss second
#define cd complex<double>
#define vcd vector<cd>
#define ldd long double
#define dbgLine cout<<"Line : "<<__LINE__<<'\n'
#define all(x) (x).begin(),(x).end()
using namespace std;
const short int __PRECISION = 10;
const ll MOD = 1e9+7;
const ll INF = 1e17 + 1101;
const ll LOGN = 17;
const ll MAXN = 1e5+5;
const ll ROOTN = 320;
const ldd PI = acos(-1);
const ldd EPS = 1e-7;
int N, M, U, V, S, T;
ll d[2][MAXN], ans;
ii dis[2][MAXN];
vii g[MAXN];
inline void Dijkstra(int s)
{
int m = (s == U ? 0 : 1);
set<ii> x;
F0Re(i, N)
d[m][i] = INF;
d[m][s] = 0;
x.insert(mp(0, s));
while(!x.empty())
{
int a = (*x.begin()).ss;
x.erase(x.begin());
for(ii p : g[a])
{
if(d[m][p.ff] > d[m][a] + p.ss)
{
x.erase(mp(d[m][p.ff], p.ff));
d[m][p.ff] = d[m][a] + p.ss;
x.insert(mp(d[m][p.ff], p.ff));
}
}
}
}
inline void SuperDijstra(int s)
{
int m = (s == S ? 0 : 1);
set<pair<ii,ll>> x;
F0Re(i, N)
dis[m][i] = mp(INF, INF);
dis[m][s] = mp(0, d[m][s]);
x.insert(mp(dis[m][s], s));
while(!x.empty())
{
int a = (*x.begin()).ss;
x.erase(x.begin());
for(ii p : g[a])
{
if(dis[m][p.ff] > mp(dis[m][a].ff + p.ss, min(d[m][p.ff],dis[m][a].ss)))
{
x.erase(mp(dis[m][p.ff], p.ff));
dis[m][p.ff] = mp(dis[m][a].ff + p.ss, min(d[m][p.ff],dis[m][a].ss));
x.insert(mp(dis[m][p.ff], p.ff));
}
}
}
}
inline void solve()
{
ii tmp = mp(INF, INF);
F0Re(i, N)
tmp = min(tmp, mp(dis[0][i].ff + dis[1][i].ff, dis[0][i].ss + dis[1][i].ss));
ans = min(ans, min(tmp.ss, d[0][V]));
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
ll i, j, k;
ans = INF;
cin>>N>>M>>S>>T>>U>>V;
while(M--)
{
cin>>i>>j>>k;
g[i].pb(mp(j,k));
g[j].pb(mp(i,k));
}
Dijkstra(U);
Dijkstra(V);
SuperDijstra(S);
SuperDijstra(T);
solve();
swap(U, V);
Dijkstra(U);
Dijkstra(V);
SuperDijstra(S);
SuperDijstra(T);
solve();
cout<<ans;
return 0;
}
