#include <bits/stdc++.h>
using namespace std;
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
/*
ID: 10002181
LANG: C++
TASK: lamps
*/
using str = string; // yay python!
using ld = long double; // or double, if TL is tight
using ll = long long;
using int64 = ll;
using db = double;
using ull = unsigned long long;
#define int ll
#define ch() getchar()
#define pc(x) putchar(x)
#define tcT template<class T
#define tcTU tcT, class U
tcT> using V = vector<T>;
tcT, size_t SZ> using AR = array<T,SZ>;
using vi = V<int>;
using vb = V<bool>;
using vpi = V<pair<int,int>>;
using vvi = V<vi>;
using vl = V<ll>;
using vd = V<ld>;
using vstr = V<str>;
#define all(x) begin(x), end(x)
#define sor(x) sort(all(x))
#define rev(x) reverse(all(x))
#define sz(x) (int)(x).size()
#define rall(x) x.rbegin(), x.rend()
#define AR array
// loops
#define F0R(i, a, b) for (int i=a; i<b;++i)
#define FOR(i, a) for (int i=0; i<a;++i)
#define FORn(i, a) for (int i=1; i<=a;++i)
#define ROF(i,a) for(int i=a-1; i >= 0;--i)
#define R0F(i,a,b) for(int i=a; i > b;--i)
#define ROFn(i,a) for(int i=a; i > 0;--i)
#define rep(a) F0R(_, a)
#define trav(i,x) for(auto& i:x)
// pairs
#define mp make_pair
#define pi pair <int, int>
#define f first
#define s second
// vectors
#define lb lower_bound
#define ub upper_bound
#define SUM(v) accumulate(all(v), 0LL)
#define MN(v) *min_element(all(v))
#define MX(v) *max_element(all(v))
#define UNIQUE(a) (a).erase(unique((a).begin(),(a).end()),(a).end())
#define eb emplace_back
#define ft front()
#define bk back()
#define ins insert
#define pf push_front
#define pb push_back
#define emt empty()
#define rsz resize
#define pob pop_back()
#define pof pop_front()
#define swp(a,b) a^=b^=a^=b
#define ts to_string
#define setIO() ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
ll MOD = 1e9+7;
const ll MAX = 100000000000;
const ll INF = 1e18; // not too close to LLONG_MAX
const ld PI = acos((ld)-1);
#ifdef _DEBUG
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif
const int dx[4] = {1,0,-1,0}, dy[4] = {0,1,0,-1}; // for every grid problem!!
tcT> bool ckmin(T& a, const T& b) {
return b < a ? a = b, 1 : 0; } // set a = min(a,b)
tcT> bool ckmax(T& a, const T& b) {
return a < b ? a = b, 1 : 0; }
tcTU> T fstTrue(T lo, T hi, U f) {
hi ++; assert(lo <= hi); // assuming f is increasing
while (lo < hi) { // find first index such that f is true
T mid = lo+(hi-lo)/2;
f(mid) ? hi = mid : lo = mid+1;
}
return lo;
}
tcTU> T lstTrue(T lo, T hi, U f) {
lo --; assert(lo <= hi); // assuming f is decreasing
while (lo < hi) { // find first index such that f is true
T mid = lo+(hi-lo+1)/2;
f(mid) ? lo = mid : hi = mid-1;
}
return lo;
}
//INPUT
#define tcTUU tcT, class ...U
tcT> void re(complex<T>& c);
tcTU> void re(pair<T,U>& p);
tcT> void re(V<T>& v);
tcT, size_t SZ> void re(AR<T,SZ>& a);
tcT> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
tcTUU> void re(T& t, U&... u) { re(t); re(u...); }
tcT> void re(complex<T>& c) { T a,b; re(a,b); c = {a,b}; }
tcTU> void re(pair<T,U>& p) { re(p.f,p.s); }
tcT> void re(V<T>& x) { trav(a,x) re(a); }
tcT> void rv(int n, V<T>& x) { x.rsz(n); re(x); }
//OUTPUT
namespace output {
tcT> void PS(V<T>& x) { FOR(i,sz(x)) cout << x[i] << " \n"[i + 1 == sz(x)];}
tcT> void W(pair<T,T>& x) { cout << x.f << ' ' << x.s << '\n'; }
tcT> void PS(bool ok) { if(ok) cout << "YES\n"; else cout << "NO\n"; }
template<class T1, class T2> void pr(const pair<T1,T2>& x);
tcT, size_t SZ> void pr(const array<T,SZ>& x);
tcT> void pr(const vector<T>& x);
tcT> void pr(const set<T>& x);
template<class T1, class T2> void pr(const map<T1,T2>& x);
tcT> void pr(const T& x) { cout << x; }
template<class Arg, class... Args> void pr(const Arg& first, const Args&... rest) {
pr(first); pr(rest...);
}
template<class T1, class T2> void pr(const pair<T1,T2>& x) {
pr("{",x.f,", ",x.s,"}");
}
tcT> void prContain(const T& x) {
pr("{");
bool fst = 1; trav(a,x) pr(!fst?", ":"",a), fst = 0;
pr("}");
}
tcT, size_t SZ> void pr(const array<T,SZ>& x) { prContain(x); }
tcT> void pr(const vector<T>& x) { prContain(x); }
tcT> void pr(const set<T>& x) { prContain(x); }
template<class T1, class T2> void pr(const map<T1,T2>& x) { prContain(x); }
void ps() { pr("\n"); } // print w/ spaces
template<class Arg> void ps(const Arg& first) { pr(first,"\n"); }
template<class Arg, class... Args> void ps(const Arg& first, const Args&... rest) {
pr(first," "); ps(rest...);
}
}
using namespace output;
template<class T,class V> void add(T& a, const V& b) {
a = (a + b) % MOD;
}
template<class T,class V> void sub(T& a, const V& b) {
a = (a - b + MOD) % MOD;
}
template<class T,class V> void mult(T& a, const V& b) {
a = a * b % MOD;
}
void setF(string fileName = "") {
ios_base::sync_with_stdio(0); cin.tie(0);
if((int)fileName.size()) {
freopen((fileName+".in").c_str(), "r", stdin);
freopen((fileName+".out").c_str(), "w", stdout);
}
}
vb bb;
vi SIEVE(int N){ // sieve in O(N logN)
vi pr;
bb.rsz(N);
bb[0] = bb[1] = true;
vi g(N);
F0R(i,2,N){
if(!bb[i]){
pr.pb(i);
for (int j = i + i; j < N; j += i) bb[j] = true;
}
}
return pr;
}
template<class T> using ordset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
struct edge{
int a;
int b;
int w;
};
ll POW(ll x, ll y,ll mod = INF){
ll res = 1LL;
x %= mod;
while(y){
if (y & 1LL)
res *= x;
res %= mod;
x = (x*x) % mod;
y >>= 1LL;
}
return res;
}
ll gauss(ll n) { return n * (n + 1ll) / 2; }
ll fact(ll x) { if(x) return x * fact(x - 1ll); return 1; }
vl fc;
void F(int N,ll MOD){
fc.rsz(N + 1);
fc[0] = 1;
FORn(i,N) fc[i] = fc[i - 1] * i * 1ll % MOD;
}
vl inv;
void I(int N,ll MOD){
inv.rsz(N + 1);
inv[N] = POW(fc[N],MOD - 2,MOD);
for (int i = N; i ;--i) inv[i - 1] = inv[i] * 1ll * i % MOD;
}
ll Cr(ll N,ll K,ll mod){
if(K < 0) return 0;
if(K > N) return 0;
return fc[N] * 1ll * inv[K] % mod * inv[N - K] % mod;
}
ll Ar(ll N,ll K,ll mod){
return fc[N] * inv[N - K] % mod;
}
ll iv(int k,ll MOD){
return POW(k,MOD-2,MOD);
}
/*
scanf("%lld", &testInteger);
printf("%lld", testInteger);
____ ____ ____ ____ ____ ____
||f |||l |||o |||p |||p ||||y ||
||__|||__|||__|||__|||__||||__||
|/__\|/__\|/__\|/__\|/__\||/__\|
**/
const int inf = (ll)1e14;
void solve(){
int N,M; cin >> N >> M;
V<vpi> A(N + 1),r(N + 1);
int S,T,U,V; cin >> U >> V >> S >> T;
while(M--){
int u,v,c; cin >> u >> v >> c;
A[u].pb({v,c});
A[v].pb({u,c});
}
auto djs = [&] (int i){
vi cost(N + 1,inf);
cost[i] = 0;
priority_queue<pi,vpi,greater<pi>>pq;
pq.push({0,i});
while(sz(pq)){
auto a = pq.top();
pq.pop();
if(a.f > cost[a.s]) continue;
trav(x,A[a.s])
if(cost[x.f] > x.s + a.f){
cost[x.f] = x.s + a.f;
pq.push({cost[x.f],x.f});
}
}
return cost;
};
vi a = djs(T);
vi b = djs(U);
vb been(N + 1);
been[V] = true;
queue<int>q;
q.push(V);
while(sz(q)){
int i = q.ft;
q.pop();
trav(x,A[i])
if(b[i] - x.s == b[x.f]){
if(!been[x.f]) q.push(x.f);
been[x.f] = true;
r[i].pb({x.f,x.s});
r[x.f].pb({i,x.s});
}
}
vvi cost(N + 1,vi(2,inf));
//ps(r);
cost[S][0] = 0;
priority_queue<vi,vvi,greater<vi>>pq;
pq.push({0,0,S});
int ans = a[S];
while(sz(pq)){
auto node = pq.top();
pq.pop();
if(node[0] > cost[node[2]][node[1]]) continue;
if(a[1]) {
ckmin(ans,cost[node[2]][1] + a[node[2]]);
trav(x,r[node[2]])
if(cost[x.f][1] > node[0]){
cost[x.f][1] = node[0];
pq.push({cost[x.f][1],1,x.f});
}
}
else{
pq.push({node[0],1,node[2]});
trav(x,A[node[2]])
if(cost[x.f][0] > node[0] + x.s){
cost[x.f][0] = node[0] + x.s;
pq.push({cost[x.f][0],0,x.f});
}
}
}
ps(ans);
}
main()
{ setIO();
solve();
}
// look out for out of bounds arrays
// And more importantly, is y a vowel? Damian:1
// <3 :L ._. <_<
// You have no idea how high I can fly
// code is my poetry
