#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pb push_back
#define all(x) begin(x), end(x)
#define sz(x) (int) (x).size()
#define f first
#define s second
#define mkp make_pair
#define pii pair<int, int>
const int N = 1e5 + 5;
int n, m, s, t, u, v;
int ds[N], dt[N], du[N], dv[N], dc[N];
vector<pii> adj[N];
priority_queue<pii, vector<pii>, greater<pii>> pq;
void calcDV(){
fill(dv, dv + n, 1e18);
dv[v] = 0;
pq.push({0, v});
while(!pq.empty()){
pii curr = pq.top(); pq.pop();
if(dv[curr.s] != curr.f) continue;
for(auto x : adj[curr.s]){
if(dv[x.s] > curr.f + x.f){
dv[x.s] = curr.f + x.f;
pq.push({dv[x.s], x.s});
}
}
}
}
void calcDU(){
fill(du, du + n, 1e18); du[u] = 0;
pq.push({0, u});
while(!pq.empty()){
pii curr = pq.top(); pq.pop();
if(du[curr.s] != curr.f) continue;
for(auto x : adj[curr.s]){
if(du[x.s] > curr.f + x.f){
du[x.s] = curr.f + x.f;
pq.push({du[x.s], x.s});
}
}
}
}
void calcDS(){
fill(ds, ds + n, 1e18);
ds[s] = 0;
pq.push({0, s});
while(!pq.empty()){
pii curr = pq.top(); pq.pop();
if(ds[curr.s] != curr.f) continue;
for(auto x : adj[curr.s]){
if(ds[x.s] > curr.f + x.f){
ds[x.s] = curr.f + x.f;
pq.push({ds[x.s], x.s});
}
}
}
}
int32_t main() {
cin.tie(0)->sync_with_stdio(0);
cin >> n >> m >> s >> t >> u >> v;
s--; t--; u--; v--;
for(int i = 0; i < m; i++){
int a, b, c;
cin >> a >> b >> c;
a--; b--;
adj[a].pb({c, b});
adj[b].pb({c, a});
}
fill(dt, dt + n, 1e18);
fill(dc, dc + n, 1e18);
calcDV();
calcDU();
calcDS();
int best = ds[t];
dt[t] = 0;
pq.push({0, t});
while(!pq.empty()){
pii curr = pq.top(); pq.pop();
if(dt[curr.s] != curr.f) continue;
for(auto x : adj[curr.s]){
if(dt[x.s] > curr.f + x.f){
dt[x.s] = curr.f + x.f;
pq.push({dt[x.s], x.s});
}
if(dt[x.s] == curr.f + x.f){
if(dt[curr.s] + ds[x.s] + x.f == best){
dc[x.s] = min({dc[x.s], du[x.s], dc[curr.s]});
}
}
}
}
fill(ds, ds + n, 1e18);
ds[s] = 0;
pq.push({0, s});
while(!pq.empty()){
pii curr = pq.top(); pq.pop();
if(ds[curr.s] != curr.f) continue;
for(auto x : adj[curr.s]){
if(ds[x.s] > curr.f + x.f){
ds[x.s] = curr.f + x.f;
pq.push({ds[x.s], x.s});
}
if(ds[x.s] == curr.f + x.f){
if(ds[curr.s] + ds[x.s] + x.f == best){
dc[x.s] = min({dc[x.s], du[x.s], dc[curr.s]});
}
}
}
}
int ans = du[v];
for(int i = 0; i < n; i++){
if(ds[i] + dt[i] == best){
ans = min(ans, dv[i] + dc[i]);
}
}
///// break
fill(dt, dt + n, 1e18);
fill(dc, dc + n, 1e18);
swap(u, v);
calcDU();
calcDV();
calcDS();
dt[t] = 0;
pq.push({0, t});
while(!pq.empty()){
pii curr = pq.top(); pq.pop();
if(dt[curr.s] != curr.f) continue;
for(auto x : adj[curr.s]){
if(dt[x.s] > curr.f + x.f){
dt[x.s] = curr.f + x.f;
pq.push({dt[x.s], x.s});
}
if(dt[x.s] == curr.f + x.f){
if(dt[curr.s] + ds[x.s] + x.f == best){
dc[x.s] = min({dc[x.s], du[x.s], dc[curr.s]});
}
}
}
}
fill(ds, ds + n, 1e18);
ds[s] = 0;
pq.push({0, s});
while(!pq.empty()){
pii curr = pq.top(); pq.pop();
if(ds[curr.s] != curr.f) continue;
for(auto x : adj[curr.s]){
if(ds[x.s] > curr.f + x.f){
ds[x.s] = curr.f + x.f;
pq.push({ds[x.s], x.s});
}
if(ds[x.s] == curr.f + x.f){
if(ds[curr.s] + ds[x.s] + x.f == best){
dc[x.s] = min({dc[x.s], du[x.s], dc[curr.s]});
}
}
}
}
for(int i = 0; i < n; i++){
if(ds[i] + dt[i] == best){
ans = min(ans, dv[i] + dc[i]);
}
}
cout << ans << '\n';
return 0;
}
