#include "bits/stdc++.h"
using namespace std;
#define fi first
#define se second
#define ll long long
#define dbg(v) cerr<<#v<<" = "<<v<<'\n'
#define vi vector<int>
#define vl vector <ll>
#define pii pair<int,int>
#define mp make_pair
#define db long double
#define pb push_back
#define all(s) s.begin(),s.end()
template < class T > T smin(T &a,T b) {if (a > b) a = b;return a;}
template < class T > T smax(T &a,T b) {if (a < b) a = b;return a;}
const int N = (int)(1e6) + 5;
ll D1[N];
ll D2[N];
ll D3[N];
ll D4[N];
vector < pii > g[N];
int n;
void Go(ll D[],int S) {
for (int i = 1;i <= n;++i)
D[i] = 1e18;
D[S] = 0;
priority_queue < pair < ll , int > , vector < pair < ll , int > > , greater < pair < ll , int > > > Q;
Q.push(mp(0,S));
while (!Q.empty()) {
const ll cost = Q.top().fi;
const int node = Q.top().se;
Q.pop();
if (cost != D[node])
continue;
for (auto it : g[node])
if (D[it.fi] > D[node] + it.se)
D[it.fi] = D[node] + it.se,Q.push(mp(D[it.fi],it.fi));
}
}
ll ans = 1e18;
vi order;
vi G[2][N];
int was[N];
void go(ll d1[],ll d2[],int who) {
static ll D[N];
for (int i = 1;i <= n;++i)
D[i] = d1[i];
for (auto u : order)
for (auto v : G[who][u])
smin(D[u],D[v]);
for (int i = 1;i <= n;++i)
smin(ans,D[i] + d2[i]);
}
int main(void)
{
int m;
int S,T,U,V;
cin>>n>>m>>S>>T>>U>>V;
while (m --) {
int a,b,c;
cin>>a>>b>>c;
g[a].pb(mp(b,c));
g[b].pb(mp(a,c));
}
Go(D1,S);
Go(D2,T);
Go(D3,U);
Go(D4,V);
queue < int > q;
q.push(S);
was[S] = 1;
const ll dist = D1[T];
while (!q.empty()) {
int node = q.front();
q.pop();
order.pb(node);
for (auto it : g[node])
if (D1[node] + it.se + D2[it.fi] == dist) {
if (!was[it.fi])
was[it.fi] = 1,q.push(it.fi);
}
}
for (int i = 1;i <= n;++i) {
for (auto it : g[i]) {
if (D1[i] + it.se + D2[it.fi] == dist)
G[0][i].pb(it.fi);
if (D1[it.fi] + it.se + D2[i] == dist)
G[1][it.fi].pb(i);
}
}
ans = D3[V];
for (int cs = 0;cs < 2;++cs) {
go(D3,D4,cs);
go(D4,D3,cs);
reverse(all(order));
go(D3,D4,cs);
go(D4,D3,cs);
reverse(all(order));
}
cout << ans << '\n';
return 0;
}
