#include <bits/stdc++.h>
using namespace std;
#define int long long
#define fi first
#define se second
#define pb push_back
#define pii pair<int, int>
#define all(x) x.begin(), x.end()
bool ckmin(int& a, int b){return b < a ? a = b, 1 : 0;}
bool ckmax(int& a, int b){return b > a ? a = b, 1 : 0;}
const int N = 2e5 + 5, mod = 1e9 + 7, INF = 1e18;
vector<pii> a[N];
int dp[N], dp2[N], dp3[N], val[N];
signed main(){
ios_base::sync_with_stdio(0), cin.tie(0);
int n, m, s, t, u, v; cin >> n >> m >> s >> t >> u >> v;
priority_queue<pii, vector<pii>, greater<pii>> pq;
for(int i = 1; i <= m; i++) {
int x, y, z; cin >> x >> y >> z;
a[x].pb({y, z});
a[y].pb({x, z});
}
for(int i = 1; i <= n; i++) dp[i] = dp3[i] = INF ;
pq.push({0, s});
dp[s] = 0;
while(!pq.empty()) {
pii p = pq.top(); pq.pop();
if(p.fi > dp[p.se]) continue;
for(auto i : a[p.se]) {
if(dp[i.fi] > p.fi + i.se) {
dp[i.fi] = p.fi + i.se;
pq.push({dp[i.fi], i.fi});
}
}
}
int mn = dp[t];
queue<int> q;
q.push(t);
val[t] = 1;
while(!q.empty()) {
int p = q.front(); q.pop();
for(auto i : a[p]) {
if(dp[i.fi] + i.se == dp[p]) {
if(!val[i.fi]) {
val[i.fi] = 1;
q.push(i.fi);
}
}
}
}
pq.push({0, u});
dp2[u] = 0;
while(!pq.empty()) {
pii p = pq.top(); pq.pop();
if(p.fi > dp2[p.se]) continue;
for(auto i : a[p.se]) {
if(dp2[i.fi] > p.fi + i.se) {
dp2[i.fi] = p.fi + i.se;
pq.push({dp2[i.fi], i.fi});
}
}
}
pq.push({0, v});
dp3[v] = 0;
while(!pq.empty()) {
pii p = pq.top(); pq.pop();
if(p.fi > dp3[p.se]) continue;
for(auto i : a[p.se]) {
if(dp3[i.fi] > p.fi + i.se) {
dp3[i.fi] = p.fi + i.se;
pq.push({dp3[i.fi], i.fi});
}
}
}
int ans = INT_MAX;
for(int i = 1; i <= n; i++) {
if(val[i]) {
ans = min(ans, mn + dp3[i]);
}
}
cout << ans << endl ;
}
