// from duckindog wth depression
#include<bits/stdc++.h>
using namespace std;
#define int long long
using pii = pair<int, int>;
using T = tuple<int, int, int>;
const int N = 1e5 + 10;
int n, m;
int s, t, U, V;
vector<pair<int, int>> ad[N];
int fs[N], ft[N];
int arr[N];
void sktra(int x) {
memset(arr, 40, sizeof arr);
priority_queue<pii, vector<pii>, greater<pii>> q;
q.emplace(arr[x] = 0, x);
while (q.size()) {
int dis, u; tie(dis, u) = q.top(); q.pop();
if (dis != arr[u]) continue;
for (auto duck : ad[u]) {
int v, w; tie(v, w) = duck;
if (arr[v] > dis + w)
q.emplace(arr[v] = dis + w, v);
}
}
}
int answer = LLONG_MAX;
int f[N][3];
void dijsktra(int x) {
memset(f, 40, sizeof f);
priority_queue<T, vector<T>, greater<T>> q;
q.emplace(f[x][0] = 0, x, 0);
while (q.size()) {
int d, u, st; tie(d, u, st) = q.top(); q.pop();
if (d != f[u][st]) continue;
for (auto duck : ad[u]) {
int v, w; tie(v, w) = duck;
bool onway = fs[u] + w + ft[v] == fs[t];
if (st != 1) {
if (f[v][st] > d + w)
q.emplace(f[v][st] = d + w, v, st);
}
if (st <= 1 && onway) {
if (f[v][1] > d)
q.emplace(f[v][1] = d, v, 1);
}
if (st == 1 && !onway) {
if (f[v][2] > d + w)
q.emplace(f[v][2] = d + w, v, 2);
}
}
}
}
int32_t main() {
cin.tie(0)->sync_with_stdio(0);
if (fopen("duck.inp", "r")) {
freopen("duck.inp", "r", stdin);
freopen("duck.out", "w", stdout);
}
cin >> n >> m;
cin >> s >> t >> U >> V;
for (int i = 1; i <= m; ++i) {
int a, b, c; cin >> a >> b >> c;
ad[a].push_back({b, c});
ad[b].push_back({a, c});
}
sktra(s);
for (int i = 1; i <= n; ++i) fs[i] = arr[i];
sktra(t);
for (int i = 1; i <= n; ++i) ft[i] = arr[i];
dijsktra(U);
answer = min({answer, f[V][0], f[V][1], f[V][2]});
dijsktra(V);
answer = min({answer, f[U][0], f[U][1], f[U][2]});
cout << answer << '\n';
}
