#include <bits/stdc++.h>
using namespace std;
#define int long long
#define eb emplace_back
#define mp make_pair
#define pb push_back
#define pp pop_back
#define endl '\n'
#define ff first
#define ss second
#define stop exit(0)
#define sz(x) (int)x.size()
#define pause system("pause")
#define all(x) (x).begin(), (x).end()
#define deb(x) cout << #x << "-" << x << endl
typedef char chr;
typedef string str;
typedef long long ll;
typedef vector<int> vii;
typedef pair<int, int> pii;
const long long INF = LLONG_MAX;
const int inf = INT_MAX;
const int mod = 998244353;
const int MOD = 1000000007;
const int dx[] = {-1,0,1,0};
const int dy[] = {0,1,0,-1};
const double PI = 2 * acos(0.0);
const int N = 1e6+5;
int n,m;
int S,T,U,V;
int a[N],b[N],c[N];
vector <vector<pii>> v(N);
int ds[N],dv[N],du[N],dt[N];
int dp1[N],dp2[N],dp3[N];
int id[N];
bool check(int a, int b, int c) {
return (ds[T] == ds[a]+c+dt[b]);
}
inline void test_case() {
cin >> n >> m;
cin >> S >> T;
cin >> U >> V;
for (int i = 1; i <= m; i++) {
cin >> a[i] >> b[i] >> c[i];
v[a[i]].pb({b[i],c[i]});
v[b[i]].pb({a[i],c[i]});
}
for (int i = 1; i <= n; i++) {
ds[i] = du[i] = dv[i] = dt[i] = INF;
}
priority_queue <pii, vector <pii>, greater<pii>> q;
q.push({0,S});
ds[S] = 0;
while (!q.empty()) {
auto [c,f] = q.top();
q.pop();
if (c != ds[f]) continue;
for (auto [to,c1]:v[f]) {
if (ds[to] > ds[f]+c1) {
ds[to] = ds[f]+c1;
q.push({ds[to],to});
}
}
}
while (!q.empty()) q.pop();
q.push({0,U});
du[U] = 0;
while (!q.empty()) {
auto [c,f] = q.top();
q.pop();
if (c != du[f]) continue;
for (auto [to,c1]:v[f]) {
if (du[to] > du[f]+c1) {
du[to] = du[f]+c1;
q.push({du[to],to});
}
}
}
while (!q.empty()) q.pop();
q.push({0,V});
dv[V] = 0;
while (!q.empty()) {
auto [c,f] = q.top();
q.pop();
if (c != dv[f]) continue;
for (auto [to,c1]:v[f]) {
if (dv[to] > dv[f]+c1) {
dv[to] = dv[f]+c1;
q.push({dv[to],to});
}
}
}
while (!q.empty()) q.pop();
q.push({0,T});
dt[T] = 0;
while (!q.empty()) {
auto [c,f] = q.top();
q.pop();
if (c != dt[f]) continue;
for (auto [to,c1]:v[f]) {
if (dt[to] > dt[f]+c1) {
dt[to] = dt[f]+c1;
q.push({dt[to],to});
}
}
}
iota(id+1,id+1+n,1);
sort(id+1,id+1+n,[](int a, int b) {
return (ds[a]<ds[b]);
});
for (int i = 1; i <= n; i++) {
dp1[i] = dp2[i] = INF;
}
for (int i = 1; i <= n; i++) {
dp1[i] = du[i];
}
for (int ii = 1; ii <= n; ii++) {
int i = id[ii];
for (auto [to,c]:v[i]) {
if (ds[to]<ds[i]) continue;
if (!check(i,to,c)) continue;
dp2[to] = min(dp2[to],dp2[i]);
dp2[to] = min(dp2[to],dp1[i]);
}
}
int res1 = INF;
for (int i = 1; i <= n; i++) {
if (dp2[i] == INF) continue;
dp3[i] = dp2[i]+dv[i];
res1 = min(res1,dp3[i]);
}
for (int i = 1; i <= n; i++) {
dp1[i] = dp2[i] = INF;
}
for (int i = 1; i <= n; i++) {
dp1[i] = dv[i];
}
for (int ii = 1; ii <= n; ii++) {
int i = id[ii];
for (auto [to,c]:v[i]) {
if (ds[to]<ds[i]) continue;
if (!check(i,to,c)) continue;
dp2[to] = min(dp2[to],dp2[i]);
dp2[to] = min(dp2[to],dp1[i]);
}
}
int res2 = INF;
for (int i = 1; i <= n; i++) {
if (dp2[i] == INF) continue;
dp3[i] = dp2[i]+du[i];
res2 = min(res2,dp3[i]);
}
int res = min(res1,res2);
int ans = min(res,du[V]);
cout << ans << endl;
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int T = 1;
// cin >> T;
while (T--) test_case();
return 0;
}
