// IN THE NAME OF ALLAH
#include<bits/stdc++.h>
using namespace std;
#define fast ios_base::sync_with_stdio(false);cin.tie(NULL)
#define wall cerr << "------------------------------------" << endl
#define pb push_back
#define pob pop_back
#define F first
#define S second
#define all(x) x.begin() , x.end()
#define scan scanf
#define print printf
#define outs(x) print("%lld " , x)
#define out(x) print("%lld\n" , x)
#define in(x) scan("%lld" , &x)
#define int ll
#define kids int tm = (tl + tr)/2; int cl = 2*v; int cr = 2*v+1
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
#pragma GCC optimize("Ofast")
typedef long long ll;
typedef pair<int , int> pii;
typedef pair<ll , ll> pll;
typedef pair<pii,int> piii;
typedef pair<pll , ll> plll;
const int N = 1e5+10;
const int K = 70+10;
const ll mod = 998244353;
const ll INF = 1e18+10;
const int P = 31;
const int lg = 25;
vector<pii> g[N];
vector<pii> gr[N];
vector<pii> rg[N];
int dp[N];
int pd[N];
int n , m;
int s , t;
int x , y;
int dis[5][N];
int mark[N];
pair<pii , int> edg[2*N];
vector<int> vec , ve;
void dfs(int v) {
mark[v] = 1;
for(auto u : gr[v])
if(!mark[u.F])
dfs(u.F);
vec.pb(v);
}
void topol() {
for(int i = 1 ; i <= ve.size() ; i++)
if(!mark[ve[i-1]])
dfs(ve[i-1]);
reverse(all(vec));
}
void dij(int v , int t) {
priority_queue<pii , vector<pii> , greater<pii>> pq;
dis[t][v] = 0;
pq.push({0 , v});
while(pq.size()) {
int v = pq.top().S;
int ww = pq.top().F;
pq.pop();
if(ww != dis[t][v])
continue;
for(auto u : g[v])
if(dis[t][u.F] > dis[t][v] + u.S) {
dis[t][u.F] = dis[t][v] + u.S;
pq.push({dis[t][u.F] , u.F});
}
}
}
void solve()
{
cin >> n >> m >> s >> t >> x >> y;
for(int i = 1 ; i <= m ; i++) {
int v , u , w;
cin >> v >> u >> w;
g[v].pb({u , w});
g[u].pb({v , w});
edg[i] = {{v , u} , w};
}
for(int i = 1 ; i <= 4 ; i++)
for(int j = 1 ; j <= n ; j++)
dis[i][j] = INF;
dij(s , 1);
dij(t , 2);
dij(x , 3);
dij(y , 4);
for(int i = 1 ; i <= m ; i++) {
int v = edg[i].F.F;
int u = edg[i].F.S;
int w = edg[i].S;
if(dis[1][v] + w + dis[2][u] == dis[1][t]) {
gr[v].pb({u , w});
rg[u].pb({v , w});
if(!mark[v]) {
mark[v] = 1;
ve.pb(v);
}
if(!mark[u]) {
mark[u] = 1;
ve.pb(u);
}
}
if(dis[1][u] + w + dis[2][v] == dis[1][t]) {
gr[u].pb({v , w});
rg[v].pb({u , w});
if(!mark[v]) {
mark[v] = 1;
ve.pb(v);
}
if(!mark[u]) {
mark[u] = 1;
ve.pb(u);
}
}
}
for(int i = 1 ; i <= n ; i++)
mark[i] = 0;
topol();
int ans = INF;
for(auto v : vec) {
dp[v] = dis[3][v];
for(auto u : rg[v])
dp[v] = min(dp[v] , dp[u.F]);
ans = min(ans , dp[v] + dis[4][v]);
}
for(int i = vec.size()-1 ; i >= 0 ; i--) {
int v = vec[i];
pd[v] = dis[3][v];
for(auto u : gr[v])
pd[v] = min(pd[v] , pd[u.F]);
ans = min(ans , pd[v] + dis[4][v]);
}
cout << min(ans , dis[3][y]) << "\n";
}
signed main()
{
int n = 1;
// cin >> n;
while(n--)
solve();
}
// CODE = LOVE
// IT'S EASY TO SEE
