#include <bits/stdc++.h>
using namespace std;
#pragma GCC target("avx2")
#pragma GCC optimize("Ofast")
//#pragma comment(linker, "/stack:200000000")
#pragma GCC target( "sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native" )
#pragma GCC optimize("unroll-loops")
/*
#pragma GCC optimize("profile-values,profile-reorder-functions,tracer")
#pragma GCC optimize("vpt")
#pragma GCC optimize("rename-registers")
#pragma GCC optimize("move-loop-invariants")
#pragma GCC optimize("unswitch-loops")
#pragma GCC optimize("function-sections")
#pragma GCC optimize("data-sections")
#pragma GCC optimize("branch-target-load-optimize")
#pragma GCC optimize("branch-target-load-optimize2")
#pragma GCC optimize("btr-bb-exclusive")
#pragma GCC optimize("inline")
#pragma GCC optimize("-fgcse")
#pragma GCC optimize("-fgcse-lm")
#pragma GCC optimize("-fipa-sra")
#pragma GCC optimize("-ftree-pre")
#pragma GCC optimize("-ftree-vrp")
#pragma GCC optimize("-fpeephole2")
#pragma GCC optimize("-ffast-math")
#pragma GCC optimize("-fsched-spec")
#pragma GCC optimize("-falign-jumps")
#pragma GCC optimize("-falign-loops")
#pragma GCC optimize("-falign-labels")
#pragma GCC optimize("-fdevirtualize")
#pragma GCC optimize("-fcaller-saves")
#pragma GCC optimize("-fcrossjumping")
#pragma GCC optimize("-fthread-jumps")
#pragma GCC optimize("-freorder-blocks")
#pragma GCC optimize("-fschedule-insns")
#pragma GCC optimize("inline-functions")
#pragma GCC optimize("-ftree-tail-merge")
#pragma GCC optimize("-fschedule-insns2")
#pragma GCC optimize("-fstrict-aliasing")
#pragma GCC optimize("-falign-functions")
#pragma GCC optimize("-fcse-follow-jumps")
#pragma GCC optimize("-fsched-interblock")
#pragma GCC optimize("-fpartial-inlining")
#pragma GCC optimize("no-stack-protector")
#pragma GCC optimize("-freorder-functions")
#pragma GCC optimize("-findirect-inlining")
#pragma GCC optimize("-fhoist-adjacent-loads")
#pragma GCC optimize("-frerun-cse-after-loop")
#pragma GCC optimize("inline-small-functions")
#pragma GCC optimize("-finline-small-functions")
#pragma GCC optimize("-ftree-switch-conversion")
#pragma GCC optimize("-foptimize-sibling-calls")
#pragma GCC optimize("-fexpensive-optimizations")
#pragma GCC optimize("inline-functions-called-once")
#pragma GCC optimize("-fdelete-null-pointer-checks")
*/
#define ll long long
#define all(x) x.begin(),x.end()
#define sz(x) (int) x.size()
#define f first
#define s second
#define ld long double
#define yes cout << "YES" << endl
#define no cout << "NO" << endl
#define pb push_back
#define dauzhan gay
#define popcount __builtin_popcount
#define int long long
const long double Eps = 1e-12;
const int max1 = 1e9 + 100;
const int min1 = -1e9 *1.4;
const ll mod1 = 1000000007;
const ll mod2 = 2000000011;
const ll mod3 = 3000000017;
const ll mod = 998244353;
const int N = 2e5 + 100;
const int B = 9000000 + 1;
const ll INF = 1e18 + 100;
//mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
ll binpow(ll x,ll y,ll md) {
if(y < 0) return 0;
if(y == 0) return 1;
if(y == 1) return x;
if(y % 2 == 0) {
ll now = binpow(x,y/2,md);
return (1ll*now*now) % md;
}
else {
ll now = binpow(x,y/2,md);
return (1ll*((1ll*now*now) % md)*x) % md;
}
}
/*
for(int i = 1;i <= n;i++) sp[0][i] = a[i];
for(int i = 1;i <= log2(n);i++) {
for(int l = 1;l <= n;l++) {
int r = l + (1 << i) - 1;
if(r > n) break;
int middle = l + (1 << (i - 1));
sp[i][l] = max(sp[i - 1][l],sp[i - 1][middle]);
}
}
int get(int l,int r) {
int g = log2(r - l + 1);
return max(sp[g][l],sp[g][r - (1 << g) + 1]);
}
*/
signed main() {
ios_base::sync_with_stdio(NULL);
cin.tie(0);
cout.tie(0);
int n,m,q,w,a,b;
cin >> n >> m >> a >> b >> q >> w;
vector <pair <int,int> > reb[n + 1];
for(int i = 1;i <= m;i++) {
int u,v,c;
cin >> u >> v >> c;
reb[v].pb({u,c});
reb[u].pb({v,c});
}
int rasta[n + 1] = {},rastb[n + 1] = {};
for(int i = 1;i <= n;i++) {
rasta[i] = INF;
rastb[i] = INF;
}
rasta[a] = 0;
rastb[b] = 0;
set <pair <int,int> > s;
s.insert({0,a});
while(!s.empty()) {
pair <int,int> v = *s.begin();
s.erase(v);
for(auto u:reb[v.s]) {
int newrast = u.s + v.f;
if(rasta[u.f] > newrast) {
s.erase({rasta[u.f],u.f});
rasta[u.f] = newrast;
s.insert({rasta[u.f],u.f});
}
}
}
s.insert({0,b});
while(!s.empty()) {
pair <int,int> v = *s.begin();
s.erase(v);
for(auto u:reb[v.s]) {
int newrast = u.s + v.f;
if(rastb[u.f] > newrast) {
s.erase({rastb[u.f],u.f});
rastb[u.f] = newrast;
s.insert({rastb[u.f],u.f});
}
}
}
int mnrast = INF;
for(int i = 1;i <= n;i++) mnrast = min(mnrast,rasta[i] + rastb[i]);
int rast[n + 1] = {};
for(int i = 1;i <= n;i++) {
rast[i] = INF;
}
rast[q] = 0;
s.insert({0,q});
while(!s.empty()) {
pair <int,int> v = *s.begin();
s.erase(v);
for(auto u:reb[v.s]) {
int newrast = v.f;
if(rasta[u.f] + u.s + rastb[v.s] == mnrast || rasta[v.s] + u.s + rastb[u.f] == mnrast) {
}
else {
newrast+=u.s;
}
if(newrast < rast[u.f]) {
s.erase({rast[u.f],u.f});
rast[u.f] = newrast;
s.insert({rast[u.f],u.f});
}
}
}
cout << rast[w] << endl;
}
