// 16.46
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define INF (1LL << 55)
#define MOD (1000 * 1000 * 1000 + 7)
#define maxn 100111
typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> pii;
ll len[maxn], d1[maxn], d2[maxn], min1[maxn], min2[maxn];
bool mark[maxn];
vector<pii> adj[maxn], here;
void find_path(int zac, ll d[]){
priority_queue<pii> pq;
for(int i = 0; i < maxn; i++)
d[i] = INF;
d[zac] = 0;
pq.push(mp(0, zac));
while(!pq.empty()){
int x = pq.top().se;
ll val = -pq.top().fi;
pq.pop();
if(val > d[x])
continue;
for(pii v : adj[x]){
if(d[v.fi] > d[x] + v.se){
d[v.fi] = d[x] + v.se;
pq.push(mp(-d[v.fi], v.fi));
}
}
}
}
void on_shortest_path(int s, int t, ll d[]){
queue<int> q;
q.push(t);
mark[t] = 1;
while(!q.empty()){
int x = q.front();
q.pop();
here.pb(mp(d[x], x));
for(pii v : adj[x]){
if(!mark[v.fi] && d[x] == d[v.fi] + v.se){
mark[v.fi] = 1;
q.push(v.fi);
}
}
}
}
int main(){
int n, m, s, t, u, v;
scanf("%d%d%d%d%d%d", &n, &m, &s, &t, &u, &v);
for(int i = 0; i < m; i++){
int a, b; ll c;
scanf("%d%d%lld", &a, &b, &c);
adj[a].pb(mp(b, c));
adj[b].pb(mp(a, c));
}
find_path(s, len);
find_path(u, d1);
find_path(v, d2);
on_shortest_path(s, t, len);
sort(here.begin(), here.end());
memset(mark, 0, sizeof(mark));
ll ans = d1[v];
for(int i = 0; i < here.size(); i++){
int x = here[i].se;
mark[x] = 1;
min1[x] = d1[x];
min2[x] = d2[x];
for(pii cur : adj[x]){
if(mark[cur.fi]){
min1[x] = min(min1[x], min1[cur.fi]);
min2[x] = min(min2[x], min2[cur.fi]);
}
}
ans = min(ans, d1[x] + min2[x]);
ans = min(ans, d2[x] + min1[x]);
}
printf("%lld\n", ans);
return 0;
}
