#include <bits/stdc++.h>
#define ll long long
#define fi first
#define se second
#define endl '\n'
#define MASK(i) (1LL << (i))
#define ull unsigned long long
#define ld long double
#define pb push_back
#define all(x) (x).begin() , (x).end()
#define BIT(x , i) ((x >> (i)) & 1)
#define TASK "task"
#define sz(s) (int) (s).size()
using namespace std;
const int mxN = 3e5 + 227;
const int inf = 1e9 + 277;
const int mod = 1e9 + 7;
const ll infll = 1e18 + 7;
const int base = 307;
const int LOG = 20;
template <typename T1, typename T2> bool minimize(T1 &a, T2 b) {
if (a > b) {a = b; return true;} return false;
}
template <typename T1, typename T2> bool maximize(T1 &a, T2 b) {
if (a < b) {a = b; return true;} return false;
}
struct item{
ll d;
int spec , u;
};
struct cmp{
bool operator()(const item &a , const item &b) {
return a.d > b.d;
}
};
int n , m , S , T , U , V;
vector<pair<int , int>> adj[mxN];
ll dp[mxN][3];
ll dist1[mxN] , dist2[mxN];
void pre()
{
memset(dist1 , 0x3f , sizeof(dist1));
priority_queue <pair<ll , int>, vector <pair<ll , int>> , greater<pair<ll , int>>> pq;
pq.push({dist1[S] = 0 , S});
while(!pq.empty()) {
int u = pq.top().se;
ll d = pq.top().fi;
pq.pop();
if(d != dist1[u]) continue;
for(auto it : adj[u]) {
int v = it.fi;
int c = it.se;
if(minimize(dist1[v] , dist1[u] + c) == true) {
pq.push({dist1[v] , v});
}
}
}
memset(dist2 , 0x3f , sizeof(dist2));
pq.push({dist2[T] = 0 , T});
while(!pq.empty()) {
int u = pq.top().se;
ll d = pq.top().fi;
pq.pop();
if(d != dist2[u]) continue;
for(auto it : adj[u]) {
int v = it.fi;
int c = it.se;
if(minimize(dist2[v] , dist2[u] + c) == true) {
pq.push({dist2[v] , v});
}
}
}
}
void solve()
{
cin >> n >> m >> S >> T >> U >> V;
for(int i = 1 ; i <= m ; i++) {
int u , v , c;
cin >> u >> v >> c;
adj[u].pb({v , c});
adj[v].pb({u , c});
}
pre();
// for(int u = 1 ; u <= n ; u++) {
// for(auto it : adj[u]) {
// int v = it.fi;
// int c = it.se;
// if(dist2[u] + dist1[v] + c == dist1[T]) {
// cout << u << ' ' << v << endl;
// }
// }
// }
memset(dp , 0x3f , sizeof(dp));
priority_queue<item , vector<item> , cmp> pq;
pq.push({0 , 0 , U});
dp[U][0] = 0;
while(!pq.empty()) {
int u = pq.top().u;
ll d = pq.top().d;
int spec = pq.top().spec;
pq.pop();
if(d != dp[u][spec]) continue;
for(auto it : adj[u]) {
int v = it.fi;
int c = it.se;
if(spec == 0) {
if(dist1[u] + dist2[v] + c == dist1[T]) {
if(minimize(dp[v][1] , d) == true) {
pq.push({d , 1 , v});
}
}
if(minimize(dp[v][0] , d + c) == true) {
pq.push({d + c , 0 , v});
}
}
if(spec == 1) {
if(dist1[u] + dist2[v] + c == dist1[T]) {
if(minimize(dp[v][1] , d) == true) {
pq.push({d , 1 , v});
}
}
if(minimize(dp[v][2] , d + c) == true) {
pq.push({d + c , 2 , v});
}
}
if(spec == 2) {
if(minimize(dp[v][2] , d + c) == true) {
pq.push({d + c , 2 , v});
}
}
}
}
ll res = min({dp[V][0] , dp[V][1] , dp[V][2]});
memset(dp , 0x3f , sizeof(dp));
pq.push({0 , 0 , U});
dp[U][0] = 0;
while(!pq.empty()) {
int u = pq.top().u;
ll d = pq.top().d;
int spec = pq.top().spec;
pq.pop();
if(d != dp[u][spec]) continue;
for(auto it : adj[u]) {
int v = it.fi;
int c = it.se;
if(spec == 0) {
if(dist2[u] + dist1[v] + c == dist1[T]) {
if(minimize(dp[v][1] , d) == true) {
pq.push({d , 1 , v});
}
}
if(minimize(dp[v][0] , d + c) == true) {
pq.push({d + c , 0 , v});
}
}
if(spec == 1) {
if(dist2[u] + dist1[v] + c == dist1[T]) {
if(minimize(dp[v][1] , d) == true) {
pq.push({d , 1 , v});
}
}
if(minimize(dp[v][2] , d + c) == true) {
pq.push({d + c , 2 , v});
}
}
if(spec == 2) {
if(minimize(dp[v][2] , d + c) == true) {
pq.push({d + c , 2 , v});
}
}
}
}
minimize(res , min({dp[V][0] , dp[V][1] , dp[V][2]}));
cout << res;
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(0);
//freopen(TASK".inp" , "r" , stdin);
//freopen(TASK".out" , "w" , stdout);
int tc = 1;
//cin >> tc;
while(tc--) {
solve();
}
return 0;
}
