#include<bits/stdc++.h>
#define ll long long
#define f first
#define s second
#define pb push_back
#define N 200005
#define mp make_pair
using namespace std;
ll ds[N],dt[N],du[N],df[N],raod[N],s,t,u,f,n,m,dp1[N],dp2[N],p[N],ans=100000000000000;
vector<pair<ll,ll> >v[N];
vector<ll>g[N],rev[N];
void dj(ll k){
vector<ll> d (n + 1, 100000000000000);
d[k] = 0;
set < pair<ll,ll> > q;
q.insert (make_pair (d[k], k));
while(!q.empty()) {
ll x = q.begin()->s;
q.erase (q.begin());
for (int i=0; i<v[x].size(); i++) {
ll to = v[x][i].f,
len = v[x][i].s;
if (d[x] + len < d[to]) {
if(q.find(mp(d[to] , to)) != q.end())q.erase(make_pair (d[to], to));
d[to] = d[x] + len;
q.insert(make_pair (d[to], to));
}
}
}
for(int i=1; i<=n; i++){
p[i] = d[i];
}
}
void dfs(ll x){
dp1[x] = 100000000000000;
dp2[x] = 100000000000000;
for(int i=0; i<rev[x].size(); i++)
dp1[x] = min(dp1[x] , dp1[rev[x][i]]);
dp1[x] = min(dp1[x] , du[x]);
ans = min(ans , dp1[x] + df[x]);
for(int i=0; i<rev[x].size(); i++)
dp2[x] = min(dp2[x] , dp2[rev[x][i]]);
dp2[x] = min(dp2[x] , df[x]);
ans = min(ans , dp2[x] + df[x]);
ans = min(ans , dp2[x] + du[x]);
for(int i=0; i<g[x].size(); i++)
if(raod[g[x][i]] <= 1)dfs(g[x][i]);
else raod[g[x][i]]--;
}
int main(){
ios::sync_with_stdio(false);
cin >> n >> m >> s >> t >> u >> f;
for(int i=1; i<=m; i++){
int x,y,z;
cin >> x >> y >> z;
v[x].pb(mp(y , z));
v[y].pb(mp(x , z));
}
dj(s);
for(int i=1; i<=n; i++)
ds[i] = p[i];
dj(t);
for(int i=1; i<=n; i++)
dt[i] = p[i];
dj(u);
for(int i=1; i<=n; i++)
du[i] = p[i];
dj(f);
for(int i=1; i<=n; i++)
df[i] = p[i];
for(int i=1; i<=n; i++)
for(int j=0; j<v[i].size(); j++)
if(ds[i] + v[i][j].s + dt[v[i][j].f] == ds[t]){
g[i].pb(v[i][j].f),
rev[v[i][j].f].pb(i);
}
for(int i=1; i<=n; i++)
raod[i] = (ll)rev[i].size();
ans = du[f];
dfs(s);
cout << ans << endl;
return 0;
}
