// #pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
#define el "\n"
#define pii pair<int, int>
#define pll pair<ll, ll>
#define fi first
#define se second
#define sqr(x) ((x) * (x))
#define FOR(i, l, r) for (int i = l; i <= (r); i++)
#define FOD(i, l, r) for (int i = l; i >= (r); i--)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) ((int)(x).size())
#define fast_io ios_base::sync_with_stdio(false); cin.tie(nullptr);
using db = long double;
using ll = long long;
using ull = unsigned long long;
using vi = vector<int>;
using vll = vector<ll>;
using vpii = vector<pii>;
using vpll = vector<pll>;
using vvi = vector<vi>;
using vvll = vector<vll>;
using vbool = vector<bool>;
using vvbool = vector<vbool>;
template<class T> inline bool chmax(T &a, T const &b) { return (a < b ? (a = b, true) : false); }
template<class T> inline bool chmin(T &a, T const &b) { return (a > b ? (a = b, true) : false); }
// #define DEBUG
#ifdef DEBUG
#include "D:\cpp\debug.h"
#else
#define debug(...)
#define debug_arr(...)
#endif
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
constexpr int N = 1E5 + 5;
constexpr int INF = 1E9 + 7;
constexpr ll INFLL = 1E18;
constexpr int MOD = 1E9 + 7; // 998244353
constexpr double EPS = 1E-10;
vpii adj[N];
ll d_u[N], d_v[N], d[N];
ll dp_u[N], dp_v[N];
int n, m, s, t, u, v;
ll res = INFLL;
void dijkstra1(int s, ll d[]) {
using T = pair<ll, int>;
priority_queue<T, vector<T>, greater<T>> pq;
fill(d, d + n + 1, INFLL);
pq.emplace(0, s);
d[s] = 0;
while (!pq.empty()) {
auto [dist, u] = pq.top();
pq.pop();
if (dist != d[u]) continue;
for (auto &[v, cost] : adj[u]) {
if (chmin(d[v], d[u] + cost)) {
pq.emplace(d[v], v);
}
}
}
}
void dijkstra2(int s, int t) {
using T = tuple<ll, int, int>;
priority_queue<T, vector<T>, greater<T>> pq;
fill(d + 1, d + n + 1, INFLL);
fill(dp_u, dp_u + n + 1, INFLL);
fill(dp_v, dp_v + n + 1, INFLL);
pq.emplace(0, s, 0);
while (!pq.empty()) {
auto [dist, x, p] = pq.top();
pq.pop();
if (d[x] == INFLL) {
d[x] = dist;
dp_u[x] = min(d_u[x], dp_u[p]);
dp_v[x] = min(d_v[x], dp_v[p]);
for (auto &[y, cost] : adj[x]) {
pq.emplace(d[x] + cost, y, x);
}
} else if (dist == d[x]) {
ll cand_u = min(d_u[x], dp_u[p]);
ll cand_v = min(d_v[x], dp_v[p]);
if (cand_u + cand_v < dp_u[x] + dp_v[x]) {
dp_u[x] = cand_u;
dp_v[x] = cand_v;
}
}
}
chmin(res, dp_u[t] + dp_v[t]);
}
void solve() {
cin >> n >> m >> s >> t >> u >> v;
while (m--) {
int a, b, c;
cin >> a >> b >> c;
adj[a].emplace_back(b, c);
adj[b].emplace_back(a, c);
}
dijkstra1(u, d_u);
dijkstra1(v, d_v);
res = d_u[v];
dijkstra2(s, t);
dijkstra2(t, s);
cout << res << el;
}
int main() {
fast_io
#define LOCAL
#ifndef LOCAL
#define PROBLEM ""
freopen(PROBLEM ".INP", "r", stdin);
freopen(PROBLEM ".OUT", "w", stdout);
#endif
int t = 1;
// cin >> t;
while (t--) solve();
}
