#include <bits/stdc++.h>
#include <bits/extc++.h>
#define StarBurstStream ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define iter(a) a.begin(), a.end()
#define riter(a) a.rbegin(), a.rend()
#define lsort(a) sort(iter(a))
#define gsort(a) sort(riter(a))
#define pb(a) push_back(a)
#define eb(a) emplace_back(a)
#define pf(a) push_front(a)
#define ef(a) emplace_front(a)
#define pob pop_back()
#define pof pop_front()
#define mp(a, b) make_pair(a, b)
#define F first
#define S second
#define mt make_tuple
#define gt(t, i) get<i>(t)
#define tomax(a, b) ((a) = max((a), (b)))
#define tomin(a, b) ((a) = min((a), (b)))
#define topos(a) ((a) = (((a) % MOD + MOD) % MOD))
#define uni(a) a.resize(unique(iter(a)) - a.begin())
using namespace std;
using namespace __gnu_pbds;
#define orz
#ifdef orz
#define print(a...)cerr<<"Line "<<__LINE__<<":",kout("[" + string(#a) + "] = ", a)
void kout() { cerr << endl; }
template<class T1, class ... T2> void kout(T1 a, T2 ... e) { cerr << a << " ", kout(e...); }
#define printv(a, b) {bool pvaspace=false; \
for(auto pva : a){ \
if(pvaspace) b << " "; pvaspace=true;\
b << pva;\
}\
b << "\n";}
#else
#define print(a...)
void kout() {}
template<class T1, class ... T2> void kout(T1 a, T2 ... e) {}
#define printv(a, b)
#endif
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;
using tiii = tuple<int, int, int>;
const ll MOD = 1000000007;
const ll MAX = 1LL << 60;
template<typename A, typename B>
ostream& operator<<(ostream& o, pair<A, B> p){
return o << '(' << p.F << ',' << p.S << ')';
}
ll ifloor(ll a, ll b){
if(b < 0) a *= -1, b *= -1;
if(a < 0) return (a - b + 1) / b;
else return a / b;
}
ll iceil(ll a, ll b){
if(b < 0) a *= -1, b *= -1;
if(a > 0) return (a + b - 1) / b;
else return a / b;
}
int n, m;
int S, T, U, V;
vector<vector<pii>> g;
vector<ll> getdis(int s){
vector<ll> dis(n + 1, MAX);
dis[s] = 0;
std::priority_queue<pll, vector<pll>, greater<>> pq;
pq.push(mp(0, s));
while(!pq.empty()){
int now = pq.top().S;
ll d = pq.top().F;
pq.pop();
if(d != dis[now]) continue;
for(pll i : g[now]){
if(d + i.S >= dis[i.F]) continue;
dis[i.F] = d + i.S;
pq.push(mp(d + i.S, i.F));
}
}
return dis;
}
int main(){
StarBurstStream
cin >> n >> m;
cin >> S >> T >> U >> V;
g.resize(n + 1);
for(int i = 0; i < m; i++){
int u, v, c;
cin >> u >> v >> c;
g[u].eb(mp(v, c));
g[v].eb(mp(u, c));
}
vector<ll> du = getdis(U), dv = getdis(V);
vector<ll> ds = getdis(S);
vector<vector<int>> tg(n + 1), rg(n + 1);
vector<ll> dpu(n + 1, MAX), dpv(n + 1, MAX);
for(int i = 1; i <= n; i++){
for(pii j : g[i]){
if(ds[i] + j.S != ds[j.F]) continue;
rg[j.F].eb(i);
}
}
queue<int> q;
vector<bool> vst(n + 1);
q.push(T);
vst[T] = true;
while(!q.empty()){
int now = q.front();
q.pop();
for(int i : rg[now]){
if(vst[i]) continue;
vst[i] = true;
q.push(i);
}
}
vector<int> in(n + 1);
for(int i = 1; i <= n; i++){
for(pii j : g[i]){
if(ds[i] + j.S != ds[j.F]) continue;
if(!vst[j.F]) continue;
tg[i].eb(j.F);
in[j.F]++;
}
}
q.push(S);
ll ans = dv[U];
while(!q.empty()){
int now = q.front();
q.pop();
dpu[now] = min(dpu[now], du[now]);
dpv[now] = min(dpv[now], dv[now]);
ans = min(ans, dpu[now] + dv[now]);
ans = min(ans, dpv[now] + du[now]);
//cerr << "test " << now << " " << dpu[now] << ',' << dv[now] << " " << dpv[now] << ',' << du[now] << "\n";
for(int i : tg[now]){
in[i]--;
dpu[i] = min(dpu[i], dpu[now]);
dpv[i] = min(dpv[i], dpv[now]);
if(in[i] == 0) q.push(i);
}
}
cout << ans << "\n";
return 0;
}
