#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<ll,ll> ii;
typedef pair<ld,ld> id;
typedef tuple<ll,ll,ll> tl;
typedef tuple<ll,ll,ll,ll> ql;
#define FOR(i, a, b) for(ll i=(a); i<=(b); i++)
#define ROF(i, a, b) for(ll i=(a); i>=(b); i--)
#define MEM(x, v) memset(x, v, sizeof(x))
#define FILL(x, n, v) fill(x, x+n, v);
#define ALL(x) x.begin(), x.end()
#define FAST ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define f first
#define s second
#define ins insert
#define e emplace
#define eb emplace_back
#define ef emplace_front
#define p push
#define pf push_front
#define pb push_back
#define mp make_pair
#define ub upper_bound
#define lb lower_bound
#define ft front
#define bk back
#define pp pop
#define ppb pop_back
#define ppf pop_front
#define db cout<<"YEET\n";
#define ct(x) cout<<x<<'\n';
const ll MOD = 1e9+7; //998244353
const ll MAXN = 1e5+5;
const ll INF = 1e18;
const ld PI = acos((ld)-1);
int main(){
FAST
ll n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
ll dist1[MAXN], dist2[MAXN];
vector<ii> adjlist[MAXN];
FOR(i,1,n) dist1[i] = dist2[i] = INF;
dist1[u] = dist2[v] = 0;
FOR(i,1,m){
ll a, b, c;
cin >> a >> b >> c;
adjlist[a].eb(b,c);
adjlist[b].eb(a,c);
}
priority_queue<ii, vector<ii>, greater<ii> > pq;
pq.e(0,u);
while (!pq.empty()){
ll dist = pq.top().f;
ll u = pq.top().s;
pq.pp();
if (dist > dist1[u]) continue;
for (auto edge : adjlist[u]){
ll v = edge.f;
ll cost = edge.s;
if (dist1[u] + cost < dist1[v]){
dist1[v] = dist1[u] + cost;
pq.e(dist1[v], v);
}
}
}
pq.e(0,v);
while (!pq.empty()){
ll dist = pq.top().f;
ll u = pq.top().s;
pq.pp();
if (dist > dist2[u]) continue;
for (auto edge : adjlist[u]){
ll v = edge.f;
ll cost = edge.s;
if (dist2[u] + cost < dist2[v]){
dist2[v] = dist2[u] + cost;
pq.e(dist2[v], v);
}
}
}
ii minuv[MAXN];
ll mindist[MAXN];
FOR(i,1,n) minuv[i] = mp(INF,INF), mindist[i] = INF;
minuv[s] = mp(dist1[s], dist2[s]);
mindist[s] = 0;
pq.e(0,s);
while (!pq.empty()){
ll dist = pq.top().f;
ll u = pq.top().s;
pq.pp();
if (dist > mindist[u]) continue;
for (auto edge : adjlist[u]){
ll v = edge.f;
ll cost = edge.s;
if (mindist[u] + cost < mindist[v]){
mindist[v] = mindist[u] + cost;
minuv[v] = mp(min(dist1[v], minuv[u].f), min(dist2[v], minuv[u].s));
pq.e(mindist[v], v);
} else if (mindist[u] + cost == mindist[v]){
ll chk1 = min(dist1[v], minuv[u].f) + min(dist2[v], minuv[u].s);
ll chk2 = minuv[v].f + minuv[v].s;
if (chk1 < chk2) minuv[v] = mp(min(dist1[v], minuv[u].f), min(dist2[v], minuv[u].s));
}
}
}
cout << min(minuv[t].f+minuv[t].s, dist1[v]);
}
