#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> ii;
typedef pair<int, ii> iii;
typedef pair<ii, int> ri3;
#define mp make_pair
#define pb push_back
#define fi first
#define sc second
#define SZ(x) (int)(x).size()
#define ALL(x) begin(x), end(x)
#define REP(i, n) for (int i = 0; i < n; ++i)
#define FOR(i, a, b) for (int i = a; i <= b; ++i)
#define RFOR(i, a, b) for (int i = a; i >= b; --i)
const int MAXN = 1e5+5;
const int MAXM = 2e5+5;
int N,M,S,T,U,V;
vector<iii> al[MAXN];
ll d[MAXN];
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> pq;
vector<ii> p[MAXN];
bool f[MAXM*2];
queue<int> q;
ll sssp(int S, int T, bool save) {
if (save) FOR(i,1,N) p[i].clear();
memset(d,-1,sizeof d);
d[S] = 0; pq.emplace(0,S);
while (!pq.empty()) {
int u = pq.top().sc; ll w = pq.top().fi; pq.pop();
for (auto v : al[u]) {
ll x = w+(f[v.sc.sc] ? 0 : v.sc.fi);
if (d[v.fi] == -1 || x < d[v.fi]) {
d[v.fi] = x;
if (save) p[v.fi].clear(), p[v.fi].push_back(ii(u,v.sc.sc));
pq.emplace(x,v.fi);
} else if (x == d[v.fi]) {
if (save) p[v.fi].push_back(ii(u,v.sc.sc));
}
}
}
//cout << "D " << S << " -> " << T << " = " << d[T] << endl;
return d[T];
}
void mark(int S, int x) {
memset(d,0,sizeof d);
q.push(S);
while (!q.empty()) {
int u = q.front(); q.pop();
for (auto v : p[u]) {
f[v.sc] = x;
if (x == 2) cout << v.fi << " -> " << u << endl;
if (!d[v.fi]) {
d[v.fi] = 1;
q.push(v.fi);
}
}
}
}
int main() {
//freopen("in.txt", "r", stdin);
ios::sync_with_stdio(false);
cin.tie(0);
cin >> N >> M;
cin >> S >> T;
cin >> U >> V;
FOR(i,0,M-1){
int A,B,C; cin >> A >> B >> C;
//cout << "E " << A << " " << B << " :: " << C << " (" << i*2 << ")" << endl;
//cout << "E " << B << " " << A << " :: " << C << " (" << i*2+1 << ")" << endl;
al[A].push_back(iii(B, ii(C,i*2)));
al[B].push_back(iii(A, ii(C,i*2+1)));
}
sssp(S,T,1);
mark(T,1);
ll ans = sssp(U,V,0);
mark(T,0);
sssp(T,S,1);
mark(S,1);
ans = min(ans, sssp(U,V,0));
cout << ans << '\n';
//mark(V,2);
}
