#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define ff first
#define ss second
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define int long long
template <class F, class _S>
bool chmin(F &u, const _S &v){
bool flag = false;
if ( u > v ){
u = v; flag |= true;
}
return flag;
}
template <class F, class _S>
bool chmax(F &u, const _S &v){
bool flag = false;
if ( u < v ){
u = v; flag |= true;
}
return flag;
}
constexpr long double EPS = 1e-12;
const int N = 1e6+50, inf = 1e17;
//int mod = 998244353
//int mod = 1000000007;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
#define rnd(l, r) uniform_int_distribution <int> (l, r)(rng)
void solve(){
int n, m;
cin >> n >> m;
int s, t;
cin >> s >> t;
int u, v;
cin >> u >> v;
vector<vector<array<int, 2>>> g(n+1);
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});
}
auto bfs = [&](int ps) -> vector<int>{
vector<int> dp(n+1, inf);
dp[ps] = 0;
priority_queue<array<int, 2>> pq;
pq.push({0, ps});
while(pq.size()){
auto [dis, ps] = pq.top();
pq.pop();
dis = -dis;
if(dis > dp[ps])continue;
for(auto [to, cost]:g[ps])
if(chmin(dp[to], dp[ps] + cost))
pq.push({-dp[to], to});
}
return dp;
};
vector<int> su, sv, ss;
su = bfs(u);
sv = bfs(v);
ss = bfs(s);
vector<int> umn(n+1, inf), vmn(n+1, inf);
umn[t] = su[t];
vmn[t] = sv[t];
priority_queue<array<int,2>> q;
q.push({ss[t], t});
int ans = su[v];
while(q.size()){
auto [dis, ps] = q.top();
q.pop();
chmin(umn[ps], su[ps]);
chmin(ans, umn[ps] + sv[ps]);
//cout << ps << ' ' << umn[ps] << ' ' << sv[ps] << '\n';
for(auto [to, cost]:g[ps]){
if(ss[to] == ss[ps] - cost && chmin(umn[to], umn[ps]))
q.push({ss[to], to});
}
}
q.push({ss[t], t});
while(q.size()){
auto [dis, ps] = q.top();
q.pop();
chmin(vmn[ps], sv[ps]);
chmin(ans, vmn[ps] + su[ps]);
//cout << ps << ' ' << vmn[ps] << ' ' << su[ps] << '\n';
for(auto [to, cost]:g[ps]){
if(ss[to] == ss[ps] - cost && chmin(vmn[to], vmn[ps]))
q.push({ss[to], to});
}
}
cout << ans << '\n';
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
int tt = 1;
//cin >> tt;
while(tt--){
solve();
}
}
