//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
//#pragma GCC optimize("Ofast,unroll-loops,fast-math,O3")
#include<bits/stdc++.h>
using namespace std;
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define sz(a) (int)a.size()
#define s second
#define f first
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
vector<pii> rid = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
vector<pii> dir = {{-1, -1}, {-1, 1}, {1, -1}, {1, 1}};
const int N = 1e6 + 1, mod = 1e9 + 7;
const ll inf = 1e18;
double eps = 1e-15;
bool flg = 0;
vector<pll> g[N];
ll d[4][N];
void djk(int x, int tp) {
set<pll> s;
d[tp][x] = 0;
s.insert({0, x});
while (sz(s)) {
x = (*s.begin()).s;
s.erase(s.begin());
for (auto [to, w]: g[x]) {
if (d[tp][to] <= d[tp][x] + w) continue;
s.erase({d[tp][to], to});
d[tp][to] = d[tp][x] + w;
s.insert({d[tp][to], to});
}
}
}
vector<int> gr[N], was(N), ord;
void dfs(int u) {
was[u] = 1;
for (int to: gr[u]) {
if (!was[to]) dfs(to);
}
ord.push_back(u);
}
void slv() {
int n, m;
cin >> n >> m;
for (int i = 1; i <= n; i++) {
for (int j = 0; j < 4; j++)
d[j][i] = inf;
}
int s, t;
cin >> s >> t;
int u, v;
cin >> u >> v;
int a[m + 1], b[m + 1], c[m + 1];
for (int i = 1; i <= m; i++) {
cin >> a[i] >> b[i] >> c[i];
g[a[i]].push_back({b[i], c[i]});
g[b[i]].push_back({a[i], c[i]});
}
djk(s, 0);
djk(t, 1);
djk(u, 2);
djk(v, 3);
ll L = d[0][t];
for (int i = 1; i <= m; i++) {
if (d[0][a[i]] + d[1][b[i]] + c[i] == L) {
//cout << a[i] << ' ' << b[i] << '\n';
gr[b[i]].push_back(a[i]);
}
if (d[0][b[i]] + d[1][a[i]] + c[i] == L) {
//cout << b[i] << ' ' << a[i] << '\n';
gr[a[i]].push_back(b[i]);
}
}
for (int i = 1; i <= n; i++) {
if (sz(gr[i]) && !was[i]) dfs(i);
}
//cout << '\n';
vector<ll> dp1(n + 1, inf), dp2(n + 1, inf);
ll ans = d[2][v];
for (int x: ord) {
dp1[x] = d[2][x];
dp2[x] = d[3][x];
for (int to: gr[x]) {
dp1[x] = min(dp1[x], dp1[to]);
dp2[x] = min(dp2[x], dp2[to]);
}
//cout << x << ' ' << dp1[x] << ' ' << dp2[x] << '\n';
ans = min(ans, d[3][x] + dp1[x]);
ans = min(ans, d[2][x] + dp2[x]);
}
cout << ans;
}
main() {
//freopen("rsq.in", "r", stdin);
//freopen("rsq.out", "w", stdout);
ios_base::sync_with_stdio(0);
cin.tie(0);
int tp = 1;
if (flg) cin >> tp;
while (tp--) {
//cout << "Case #" << cur++ << ": ";
slv();
}
}
//wenomechainsama
