#include<bits/stdc++.h>
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
typedef long long ll;
#define int ll
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define pb push_back
#define all(x) x.begin(), x.end()
#define sz(x) (int)x.size()
#define mispertion ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0)
#define F first
#define S second
#define getlast(s) (*s.rbegin())
#define debg cout << "OK\n"
const ld PI = 3.1415926535;
const int N = 2e5 + 6;
const int M = 7e6 + 1;
const int mod = 1e9+7;
const int infi = INT_MAX;
const ll infl = LLONG_MAX;
const int P = 31;
int mult(int a, int b) {
return a * 1LL * b % mod;
}
int sum(int a, int b) {
if (a + b < 0)
return a + b + mod;
if (a + b >= mod)
return a + b - mod;
return a + b;
}
ll binpow(ll a, ll n) {
if (n == 0)
return 1;
if (n % 2 == 1) {
return binpow(a, n - 1) * a % mod;
} else {
ll b = binpow(a, n / 2);
return b * b % mod;
}
}
vector<pii> g[N];
vector<int> ng[N], pss[N], poryadok;
int dfr[N], dto[N], ds[N];
void dfs(int v, vector<int> &used){
used[v] = 1;
for(auto u : pss[v]){
ng[u].pb(v);
if(!used[u])
dfs(u, used);
}
}
void dfs1(int v, vector<int> &used){
used[v] = 1;
for(auto u : ng[v]){
if(!used[u])
dfs1(u, used);
}
poryadok.pb(v);
}
void solve(){
int n, m;
cin >> n >> m;
int s, t;
cin >> s >> t;
int fr, to;
cin >> fr >> to;
for(int i = 0; i < m; i++){
int u, v, w;
cin >> u >> v >> w;
g[u].pb({v, w});
g[v].pb({u, w});
}
set<pii> st;
for(int i = 1; i <= n; i++)
ds[i] = infl, dfr[i] = infl, dto[i] = infl;
ds[s] = 0;
st.insert({ds[s], s});
while(!st.empty()){
int v = (*st.begin()).S;
st.erase(st.begin());
for(auto e : g[v]){
int u = e.F, w = e.S;
if(ds[u] == ds[v] + w)
pss[u].pb(v);
if(ds[u] > ds[v] + w){
st.erase({ds[u], u});
ds[u] = ds[v] + w;
pss[u].clear();
pss[u].pb(v);
st.insert({ds[u], u});
}
}
}
dfr[fr] = 0;
st.insert({dfr[fr], fr});
while(!st.empty()){
int v = (*st.begin()).S;
st.erase(st.begin());
for(auto e : g[v]){
int u = e.F, w = e.S;
if(dfr[u] > dfr[v] + w){
st.erase({dfr[u], u});
dfr[u] = dfr[v] + w;
st.insert({dfr[u], u});
}
}
}
dto[to] = 0;
st.insert({dto[to], to});
while(!st.empty()){
int v = st.begin()->S;
st.erase(st.begin());
for(auto e : g[v]){
int u = e.F, w = e.S;
if(dto[u] > dto[v] + w){
st.erase({dto[u], u});
dto[u] = dto[v] + w;
st.insert({dto[u], u});
}
}
}
vector<int> used(n + 1, 0);
dfs(t, used);
used.assign(n + 1, 0);
dfs1(s, used);
reverse(all(poryadok));
vector<int> mn(n + 1, infl);
vector<int> mn1(n + 1, infl);
for(int i = 1; i <= n; i++)
mn[i] = dfr[i], mn1[i] = dto[i];
int ans = dfr[to];
for(auto v : poryadok){
for(auto u : ng[v]){
mn[u] = min(mn[u], mn[v]);
mn1[u] = min(mn1[u], mn1[v]);
}
ans = min(ans, min(mn[v] + dto[v], mn1[v] + dfr[v]));
}
cout << ans << '\n';
}
signed main() {
mispertion;
int t = 1;
//cin >> t;
while(t--){
solve();
}
return 0;
}
