#include <bits/stdc++.h>
using namespace std;
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
#define ordered_set tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update>
#pragma GCC optimize("Ofast,unroll-loops,fast-math")
#pragma GCC target("popcnt")
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<ll,ll> pll;
#define sz size()
#define ff first
#define ss second
#define all(a) a.begin(),a.end()
#define pb push_back
const int mod = ll(1e9)+7; //(b + (a%b)) % b (to mod -1%(10^9+7) correctly in c++ its -1 but its suppose to be 10^9+6
const ll MOD = 998244353; // (a%mod)*(binpow(b,mod-2,mod) = (a/b)%mod
const int N = ll(5e5)+100;
const int M = ll(2e5) + 100;
const long long inf = 5e18;
const long double eps = 1e-15L;
ll lcm(ll a, ll b) { return (a / __gcd(a,b))*b; }
ll binpow(ll a, ll b, ll m) { ll res=1; a %= m; while(b>0){ if(b&1)res=(res * a) % m; a=(a * a) % m; b/=2; } return res%m;}
void Freopen(string Key){ freopen((Key+".in").c_str(), "r", stdin); freopen((Key+".out").c_str(), "w", stdout); }
int n, m, s, t, U, V;
vector<long long> disu(N), disv(N);
vector<pair<long long, long long> > dist(N), diss(N);
vector<pair<int, int> > g[N];
void djik(vector<long long>& dis, int u) {
for(int i = 1; i <= n; i ++) dis[i] = inf;
dis[u] = 0;
set<pair<long long, int> > st;
st.insert({dis[u], u});
while(!st.empty()) {
int v = (*st.begin()).ss;
st.erase(st.begin());
for(auto to : g[v]) {
if(dis[to.ff] > dis[v] + to.ss) {
if(dis[to.ff] != inf) st.erase({dis[to.ff], to.ff});
dis[to.ff] = dis[v] + to.ss;;
st.insert({dis[to.ff], to.ff});
}
}
}
}
void Baizho() {
cin>>n>>m>>s>>t>>U>>V;
for(int i = 1; i <= m; i ++) {
int a, b, c; cin>>a>>b>>c;
g[a].pb({b, c});
g[b].pb({a, c});
}
djik(disu, U); djik(disv, V);
for(int i = 1; i <= n; i ++) diss[i] = {inf, inf};
diss[s] = {0, disu[s]};
set<pair<long long, int> > st;
st.insert({diss[s].ff, s});
while(!st.empty()) {
int v = (*st.begin()).ss;
st.erase(st.begin());
for(auto to : g[v]) {
if(diss[to.ff].ff >= diss[v].ff + to.ss) {
if(diss[to.ff].ff != inf) st.erase({diss[to.ff].ff, to.ff});
diss[to.ff] = {diss[v].ff + to.ss, min(disu[to.ff], diss[v].ss)};
st.insert({diss[to.ff].ff, to.ff});
} else if(diss[to.ff].ff == diss[v].ff + to.ss) {
diss[to.ff].ss = min(diss[to.ff].ss, diss[v].ss);
}
}
}
for(int i = 1; i <= n; i ++) dist[i] = {inf, inf};
dist[t] = {0, disv[t]};
st.insert({dist[t].ff, t});
while(!st.empty()) {
int v = (*st.begin()).ss;
st.erase(st.begin());
for(auto to : g[v]) {
if(dist[to.ff].ff >= dist[v].ff + to.ss) {
if(dist[to.ff].ff != inf) st.erase({dist[to.ff].ff, to.ff});
dist[to.ff] = {dist[v].ff + to.ss, min(disv[to.ff], dist[v].ss)};
st.insert({dist[to.ff].ff, to.ff});
} else if(dist[to.ff].ff == dist[v].ff + to.ss) {
dist[to.ff].ss = min(dist[to.ff].ss, dist[v].ss);
}
}
}
long long ans = disv[U];
// cout<<diss[t].ff<<endl;
for(int a = 1; a <= n; a ++) {
// cout<<diss[a].ff<<" "<<dist[a].ff<<" "<<a<<endl;
if(diss[a].ff + dist[a].ff == diss[t].ff) {
// cout<<a<<" "<<diss[a].ss<<" "<<dist[a].ss<<endl;
ans = min(ans, diss[a].ss + dist[a].ss);
}
}
for(int i = 1; i <= n; i ++) diss[i] = {inf, inf};
diss[s] = {0, disv[s]};
st.insert({diss[s].ff, s});
while(!st.empty()) {
int v = (*st.begin()).ss;
st.erase(st.begin());
for(auto to : g[v]) {
if(diss[to.ff].ff >= diss[v].ff + to.ss) {
if(diss[to.ff].ff != inf) st.erase({diss[to.ff].ff, to.ff});
diss[to.ff] = {diss[v].ff + to.ss, min(disv[to.ff], diss[v].ss)};
st.insert({diss[to.ff].ff, to.ff});
} else if(diss[to.ff].ff == diss[v].ff + to.ss) {
diss[to.ff].ss = min(diss[to.ff].ss, diss[v].ss);
}
}
}
for(int i = 1; i <= n; i ++) dist[i] = {inf, inf};
dist[t] = {0, disu[t]};
st.insert({dist[t].ff, t});
while(!st.empty()) {
int v = (*st.begin()).ss;
st.erase(st.begin());
for(auto to : g[v]) {
if(dist[to.ff].ff >= dist[v].ff + to.ss) {
if(dist[to.ff].ff != inf) st.erase({dist[to.ff].ff, to.ff});
dist[to.ff] = {dist[v].ff + to.ss, min(disu[to.ff], dist[v].ss)};
st.insert({dist[to.ff].ff, to.ff});
} else if(dist[to.ff].ff == dist[v].ff + to.ss) {
dist[to.ff].ss = min(dist[to.ff].ss, dist[v].ss);
}
}
}
for(int a = 1; a <= n; a ++) {
// cout<<diss[a].ff<<" "<<dist[a].ff<<" "<<a<<endl;
if(diss[a].ff + dist[a].ff == diss[t].ff) {
ans = min(ans, diss[a].ss + dist[a].ss);
}
}
cout<<ans;
}
signed main() {
// Freopen("nondec");
ios_base::sync_with_stdio(false);
cin.tie(0);cout.tie(0);
// precalc();
int ttt = 1;
// cin>>ttt;
for(int i=1; i<=ttt; i++) {Baizho(); }
}
