#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 mp make_pair
#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) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#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 <typename T>
using heap = priority_queue<T>;
template <typename T>
using min_heap = priority_queue<T, vector<T>, greater<T>>;
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 = 4E18;
constexpr int MOD = 1E9 + 7; // 998244353
constexpr double EPS = 1E-10;
using Edge = tuple<int, int, int>;
vpii adj[N];
vi dag[N];
int in[N];
ll d_s[N], d_u[N], d_v[N], d[N];
ll dp[N], dp_u[N], dp_v[N];
int n, m, s, t, u, v;
void dijkstra(int s, ll d[]) {
min_heap<pair<ll, int>> pq;
fill(d + 1, 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, w] : adj[u]) {
if (chmin(d[v], d[u] + w)) {
pq.emplace(d[v], v);
}
}
}
}
void solve() {
cin >> n >> m >> s >> t >> u >> v;
vector<Edge> edges;
while (m--) {
int a, b, w;
cin >> a >> b >> w;
adj[a].emplace_back(b, w);
adj[b].emplace_back(a, w);
edges.emplace_back(a, b, w);
}
dijkstra(s, d_s);
dijkstra(u, d_u);
dijkstra(v, d_v);
for (auto &[a, b, w] : edges) {
if (d_s[a] + w == d_s[b]) {
dag[a].push_back(b);
in[b]++;
}
if (d_s[b] + w == d_s[a]) {
dag[b].push_back(a);
in[a]++;
}
}
vi topo;
queue<int> q;
q.push(s);
while (!q.empty()) {
int x = q.front();
q.pop();
topo.push_back(x);
for (int y : dag[x]) {
if (--in[y] == 0) {
q.push(y);
}
}
}
fill(all(dp), INFLL);
fill(all(dp_u), INFLL);
fill(all(dp_v), INFLL);
dp_u[s] = d_u[s];
dp_v[s] = d_v[s];
dp[s] = dp_u[s] + dp_v[s];
for (int x : topo) {
chmin(dp[x], min(dp_u[x] + d_v[x], dp_v[x] + d_u[x]));
for (int y : dag[x]) {
chmin(dp[y], dp[x]);
chmin(dp_u[y], min(dp_u[x], d_u[y]));
chmin(dp_v[y], min(dp_v[x], d_v[y]));
}
}
cout << min(dp[t], d_u[v]) << 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();
}
