#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define is insert
#define ll long long
#define V vector
#define MS multiset
#define PL pair<ll, ll>
#define F first
#define S second
#define PQ priority_queue
#define f0r(i, begin, end) for (ll i = begin; i < end; i ++)
#define For(i, end, begin) for (ll i = end; i > begin; i --)
#define all(x) x.begin(), x.end()
#define INF 1000000000000000000
#define inf 1000000000
#define MOD 1000000007
#define len(x) (ll)x.size()
#define fileread(file) ifstream fin; fin.open((string)file + ".in"); ofstream fout; fout.open((string)file + ".out")
#define fastio ios_base::sync_with_stdio(0LL); cin.tie(nullptr)
template<typename T> istream& operator>>(istream& in, V<T>& a) {for(auto &x : a) in >> x; return in;};
template<typename T> ostream& operator<<(ostream& out, V<T>& a) {for(auto &x : a) out << x << ' '; return out;};
const ll MAX_N = 10; // 1e5
ll udist[MAX_N], vdist[MAX_N];
tuple<ll, ll, ll> optimal[MAX_N]; // (Distance, best distance from u to v w/ pass, best distance from u to v w/ pass passing through pos)
ll N, M, s, t, u, v;
V<PL> conn[MAX_N];
int main () {
cin >> N >> M >> s >> t >> u >> v;
s --; t --; u --; v --;
f0r (i, 0, M) {
ll a, b, c; cin >> a >> b >> c;
a --; b --;
conn[a].pb({b, c});
conn[b].pb({a, c});
}
f0r (i, 0, N) {
udist[i] = vdist[i] = INF;
optimal[i] = make_tuple(INF, INF, INF);
}
udist[u] = 0; vdist[v] = 0;
using T = PL;
PQ<T, vector<T>, greater<T>> altpq;
altpq.push({0, u});
while (altpq.size()) {
ll cdist;
ll node;
tie(cdist, node) = altpq.top();
altpq.pop();
if (cdist != udist[node]) continue;
for (pair<ll, ll> i : conn[node]) {
if (cdist + i.second < udist[i.first]) {
altpq.push({udist[i.first] = cdist + i.second, i.first});
}
}
}
altpq.push({0, v});
while (altpq.size()) {
ll cdist;
ll node;
tie(cdist, node) = altpq.top();
altpq.pop();
if (cdist != vdist[node]) continue;
for (pair<ll, ll> i : conn[node]) {
if (cdist + i.second < vdist[i.first]) {
altpq.push({vdist[i.first] = cdist + i.second, i.first});
}
}
}
ll ans = udist[v];
using X = pair<tuple<ll, ll, ll>, ll>;
PQ<X, vector<X>, greater<X>> pq;
pq.push({{0, udist[v], vdist[s] + udist[s]}, s});
optimal[s] = {0, udist[v], vdist[s] + udist[s]};
while (pq.size()) {
tuple<ll, ll, ll> score = pq.top().F; ll pos = pq.top().S;
ll dist, optdist, ridedist;
tie(dist, optdist, ridedist) = score;
pq.pop();
if (score != optimal[pos]) continue;
for (pair<ll, ll> i : conn[pos]) {
ll newpos = i.F, cost = i.S;
ll potov = dist + cost;
ll potdist = min(ridedist - vdist[pos] + vdist[newpos], udist[newpos] + vdist[newpos]);
ll potopt = min(optdist, potdist);
if (make_tuple(potov, potdist, potopt) < optimal[newpos]) {
pq.push({optimal[newpos] = {potov, potopt, potdist}, newpos});
}
}
}
ans = min(ans, get<1>(optimal[t]));
f0r (i, 0, N) {
optimal[i] = make_tuple(INF, INF, INF);
}
swap (s, t);
pq.push({{0, udist[v], vdist[s] + udist[s]}, s});
optimal[s] = {0, udist[v], vdist[s] + udist[s]};
while (pq.size()) {
tuple<ll, ll, ll> score = pq.top().F; ll pos = pq.top().S;
ll dist, optdist, ridedist;
tie(dist, optdist, ridedist) = score;
pq.pop();
if (score != optimal[pos]) continue;
for (pair<ll, ll> i : conn[pos]) {
ll newpos = i.F, cost = i.S;
ll potov = dist + cost;
ll potdist = min(ridedist - vdist[pos] + vdist[newpos], udist[newpos] + vdist[newpos]);
ll potopt = min(optdist, potdist);
if (make_tuple(potov, potdist, potopt) < optimal[newpos]) {
pq.push({optimal[newpos] = {potov, potopt, potdist}, newpos});
}
}
}
ans = min(ans, get<1>(optimal[t]));
cout << ans << endl;
}
