#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#pragma GCC target ("avx2")
#pragma GCC optimization ("O3")
#pragma GCC optimization ("unroll-loops")
#pragma comment(linker, "/stack:200000000")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
//turn on extra precision
//#pragma GCC target("fpmath=387")
using namespace std;
using namespace __gnu_pbds;
using str = string;
using ll = long long;
using pii = pair <int,int>;
using pll = pair <ll,ll>;
using vi = vector <int>;
using vll = vector <ll>;
using vpii = vector <pii>;
using vpll = vector <pll>;
template<class A, class B>
ostream& operator<<(ostream& os, const pair<A, B> &p) {
os << '(' << p.first << ',' << p.second << ')';
return os;
}
template<class T>
ostream& operator<<(ostream& os, const vector<T> &v) {
bool van = 1; os << '{';
for(auto &i : v) { if(!van) os << ", "; os << i; van = 0; }
os << '}'; return os;
}
template<class T, size_t sz>
ostream& operator<<(ostream&os, const array<T,sz> &arr) {
bool fs = 1; os << '{';
for(auto &i : arr) { if(!fs) os << ", "; os << i; fs = 0; }
os << '}'; return os;
}
#define mp make_pair
#define fi first
#define se second
#define fs first.second
#define ss second.second
#define ff first.first
#define sf second.first
#define newl '\n'
#define all(x) x.begin(), x.end()
#define watch(x) cerr << (#x) << " is : " << (x) << newl
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
template <class T>
ll quickpow(ll num1, ll num2, const T MOD) {
assert(num2 >= 0); ll ans = 1;
for(; num2; num2>>=1, num1 = num1 * num1 % MOD) if(num2 & 1) ans = ans * num1 % MOD;
return ans;
}
// end of Template
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
vector<vector<pair<int,int>>> adj(n+1);
for(int a, b, c; m--; ) {
cin >> a >> b >> c;
adj[a].emplace_back(b, c);
adj[b].emplace_back(a, c);
}
const ll INF = 1e17;
vector<vector<ll>> dist(4, vector<ll>(n+1, INF));
const auto dijkstra = [&n, &adj](vector<ll> &dist, int x) -> void {
vector<bool> vis(n+1);
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> q;
q.emplace(0, x);
dist[x] = 0;
for(; !q.empty(); ) {
auto [d, node] = q.top();
q.pop();
if(vis[node]) continue;
vis[node] = true;
for(auto &[nex, c] : adj[node]) {
if(dist[nex] > dist[node] + c) {
dist[nex] = dist[node] + c;
q.emplace(dist[nex], nex);
}
}
}
};
dijkstra(dist[0], s);
dijkstra(dist[1], t);
dijkstra(dist[2], u);
dijkstra(dist[3], v);
ll ans = dist[2][v], opt = dist[0][t];
const auto solve = [&](int x, int y) -> void {
priority_queue <pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> q;
for(int i = 1; i <= n; ++i) q.emplace(dist[0][i], i);
vector<ll> dp(n+1, INF);
for(; !q.empty();) {
auto [d, i] = q.top();
q.pop();
if(dist[0][i] + dist[1][i] != opt) continue;
dp[i] = dist[x][i];
for(auto &[nex, c] : adj[i]) {
if(dist[0][i] == dist[0][nex] + c) {
dp[i] = min(dp[i], dp[nex]);
}
}
ans = min(ans, dp[i] + dist[y][i]);
}
};
solve(2, 3);
solve(3, 2);
cout << ans << newl;
return 0;
}
