/*---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---*/
#include "bits/stdc++.h"
using namespace std;
#ifdef LOCAL
#include "algo/debug.h"
#else
#define dbg(x...)
#endif
#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define rrep(a, b, c) for(int a = (b); a > c; --a)
#define each(a, b) for(auto& a : b)
#define sz(x) (int)(x).size()
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define vi vector<int>
#define ar array
template<class T> using V = vector<T>;
template<class T> using pq = priority_queue<T>;
template<class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
#define lb lower_bound
#define ub upper_bound
#define pb push_back
#define eb emplace_back
#define rsz resize
#define bk back()
#define pi pair<int, int>
#define pl pair<ll, ll>
#define mp make_pair
#define f first
#define s second
#define pct(x) __builtin_popcount(x)
constexpr int fsb(int x) {return __builtin_ffs(x) - 1;} // first set bit
constexpr int log2(int x) {return x == 0 ? 0 : 31-__builtin_clz(x);} // floor(log2(x))
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
template <class T> bool umin(T& a, const T& b){return b<a?a=b, 1:0;}
template <class T> bool umax(T& a, const T& b){return a<b?a=b, 1:0;}
const int d4i[4]={-1, 0, 1, 0}, d4j[4]={0, 1, 0, -1};
const int d8i[8]={-1, -1, 0, 1, 1, 1, 0, -1}, d8j[8]={0, 1, 1, 1, 0, -1, -1, -1};
using ll = long long;
using ld = long double;
using str = string;
const int inf = (int)1e9 + 5;
const ll infl = (ll)1e18 + 5;
const ld PI = acos((ld)-1);
const int MOD = 1e9 + 7;
const int N = 1e5 + 10;
/*---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---XXX---*/
int n, m, s, t, u, v;
V<V<pi>> g(N);
V<vi> ad(N);
void solve(){
cin >> n >> m >> s >> t >> u >> v;
--s; --t; --u; --v;
rep(i, 0, m){
int a, b, c; cin >> a >> b >> c;
g[--a].eb(--b, c);
g[b].eb(a, c);
}
// DIJkstra
pqg <pl> pq;
V<ll> d(n, infl);
V<vi> p(n);
pq.emplace(d[s] = 0, s);
V<bool> vis(n);
while(!pq.empty()){
auto [od, x] = pq.top(); pq.pop();
if(d[x] != od) continue;
for(auto [y, e] : g[x]){
if(umin(d[y], od + e)){
p[y].clear();
pq.emplace(d[y], y);
}
if(d[y] == od + e){
p[y].eb(x);
}
}
}
function<void(int)> dfs = [&](int s){
vis[s] = 1;
each(x, p[s]) if(!vis[x]){
dfs(x);
}
};
dfs(t);
rep(i, 0, n){
if(!vis[i]){
p[i].clear(); continue;
}
rep(j, 0, sz(p[i])){
auto &x = p[i][j];
if(!vis[x]){
swap(x, p[i].bk);
p[i].pop_back(); --j;
}
}
}
rep(i, 0, n) if(vis[i]){
each(x, p[i]){
ad[x].eb(i);
}
}
d = V<ll> (3*n, infl);
pq.emplace(d[u] = 0, u);
while(!pq.empty()){
auto [od, x] = pq.top(); pq.pop();
if(d[x] != od) continue;
int zx = x;
while(x >= n) x -= n;
if(zx < 2*n){
for(auto y : ad[x]){
if(umin(d[y += n], od)){
pq.emplace(d[y], y);
}
}
}
if(zx < n || zx >= 2*n){
for(auto y : p[x]){
if(umin(d[y += 2*n], od)){
pq.emplace(d[y], y);
}
}
}
for(auto [y, e] : g[x]){
if(umin(d[y], od + e)){
pq.emplace(d[y], y);
}
}
}
cout << min({d[v], d[v+n], d[v+2*n]}) << '\n';
}
signed main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
solve();
}
