/*
Unknown's C++ Template (v3.2)
*/
#include "bits/stdc++.h"
using namespace std;
#define int long long
using ll = long long;
using ld = long double;
using ii = pair<int, int>;
using vi = vector<int>;
using vii = vector<ii>;
using vvi = vector<vi>;
using vvii = vector<vii>;
template <class T> using maxpq = priority_queue<T>;
template <class T> using minpq = priority_queue<T, vector<T>, greater<T>>;
#define pb push_back
#define all(x) x.begin(), x.end()
#define sz(x) (int)x.size()
#define mid ((l+r)>>1)
#define fi first
#define se second
#ifdef LOCAL
#define debug(x) cout << #x << " = " << x << "\n";
#else
#define debug(x) ;
#endif
template <class A, class B>
ostream& operator << (ostream& out, pair<A, B> x)
{ out << "(" << x.first << ", " << x.second << ")"; return out; }
template <class T>
ostream& operator << (ostream& out, vector<T> x){
out << "[";
for (int i=0; i<sz(x); i++) { out << (i ? ", " : "") << x[i]; }
out << "]"; return out;
}
template <class T>
istream& operator >> (istream& in, vector<T> &x){
for (auto &i: x) in >> i;
return in;
}
const ld PI = acos(-1.0);
const int allmod[3] = {(int)1e9+7, 998244353, (int)1e9+9};
const int mod = allmod[0];
const int maxn = 2e5 + 64;
const ll inf = 1e18;
const ld eps = 1e-6;
const int multitest = 0;
int n, m;
int s, t, a, b;
vi dist_u, dist_v, dist_s, dist_t;
vi dps, dpt;
vector<pair<ii, int>> edges;
vvii adj, dag;
void dfs(int x){
dps[x] = dist_s[x];
dpt[x] = dist_t[x];
for (auto [k, w]: dag[x]){
if (dps[k] == inf+1) dfs(k);
dps[x] = min(dps[x], dps[k]);
dpt[x] = min(dpt[x], dpt[k]);
}
}
void main_program(){
cin >> n >> m;
cin >> s >> t >> a >> b;
s--; t--; a--; b--;
dist_u.assign(n, inf); dist_v.assign(n, inf);
dist_s.assign(n, inf); dist_t.assign(n, inf);
edges.resize(m);
adj.resize(n); dag.resize(n);
dps.assign(n, inf+1);
dpt.assign(n, inf+1);
for (int i = 0; i < m; i++){
int x, y, w; cin >> x >> y >> w;
x--; y--;
edges[i] = {{x, y}, w};
adj[x].emplace_back(y, w);
adj[y].emplace_back(x, w);
}
// debug(adj);
//=== DIJKSTRA FROM U ===//
{
minpq<ii> q; q.emplace(0, s); dist_u[s] = 0;
while (!q.empty()){
auto [d, x] = q.top(); q.pop();
if (dist_u[x] != d) continue;
for (auto [k, w]: adj[x]){
if (dist_u[k] > d + w){
dist_u[k] = d + w;
q.emplace(d + w, k);
}
}
}
// debug(dist_u);
}
//=== DIJKSTRA FROM V ===//
{
minpq<ii> q; q.emplace(0, t); dist_v[t] = 0;
while (!q.empty()){
auto [d, x] = q.top(); q.pop();
if (dist_v[x] != d) continue;
for (auto [k, w]: adj[x]){
if (dist_v[k] > d + w){
dist_v[k] = d + w;
q.emplace(d + w, k);
}
}
}
// debug(dist_v);
}
//=== DIJKSTRA FROM S ===//
{
minpq<ii> q; q.emplace(0, a); dist_s[a] = 0;
while (!q.empty()){
auto [d, x] = q.top(); q.pop();
if (dist_s[x] != d) continue;
for (auto [k, w]: adj[x]){
if (dist_s[k] > d + w){
dist_s[k] = d + w;
q.emplace(d + w, k);
}
}
}
// debug(dist_s);
}
//=== DIJKSTRA FROM T ===//
{
minpq<ii> q; q.emplace(0, b); dist_t[b] = 0;
while (!q.empty()){
auto [d, x] = q.top(); q.pop();
if (dist_t[x] != d) continue;
for (auto [k, w]: adj[x]){
if (dist_t[k] > d + w){
dist_t[k] = d + w;
q.emplace(d + w, k);
}
}
}
// debug(dist_t);
}
int sp = dist_u[t];
for (auto [e, w]: edges){
int i, j; tie(i, j) = e;
if (dist_u[i] + w + dist_v[j] == sp) dag[i].emplace_back(j, w);
if (dist_u[j] + w + dist_v[i] == sp) dag[j].emplace_back(i, w);
}
// debug(dag);
dfs(s);
// debug(dps); debug(dpt);
int res = dist_s[b];
for (int i = 0; i < n; i++) res = min(res, dist_s[i] + dpt[i]);
for (int i = 0; i < n; i++) res = min(res, dist_t[i] + dps[i]);
cout << res << "\n";
}
void pre_main(){
}
signed main(){
#ifdef LOCAL
auto stime = chrono::high_resolution_clock::now();
#endif
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#ifndef ONLINE_JUDGE
if (fopen(".inp", "r")){
freopen(".inp", "r", stdin);
freopen(".out", "w", stdout);
}
#endif
int T = 1; if (multitest) cin >> T;
pre_main();
while (T--) main_program();
#ifdef LOCAL
auto etime = chrono::high_resolution_clock::now();
auto duration = chrono::duration_cast<chrono::milliseconds>(etime-stime).count();
cout << "\n[" << duration << "ms]\n";
#endif
}
