#include <bits/stdc++.h>
#define endl '\n'
#define ll long long
#define pb push_back
#define pf push_front
#define mp make_pair
#define fi first
#define se second
#define INF INT_MAX
#define ENF INT_MIN
#define llINF 1e17
#define loop(i,n) for(int i=1 ; i<=n ; i++)
#define loop0(i,n) for(int i=0 ; i<n ; i++)
#define debug(arr, n) for(int i=1 ; i<=n ; i++) cout << i << ": " << arr[i] << endl;
#define debug0(arr, n) for(int i=0 ; i<n ; i++) cout << i << ": " << arr[i] << endl;
#define mem(a,b) memset(a, b, sizeof(a))
#define pllll pair<ll,ll>
#define OUT(x) if(x) cout << "YES\n"; else cout << "NO\n";
using namespace std;
const int N = 1e5 + 5;
ll n,m,s,t,u,v;
vector<pllll> adj[N];
ll dist[N], du[N], dv[N], d[N];
set<ll> par[N];
bool vis[N];
ll ans=llINF;
pllll dp[N];
int main(){
ios_base::sync_with_stdio(false); cin.tie(NULL);
cin >> n >> m >> s >> t >> u >> v;
loop(i,m){
ll t1, t2, t3;
cin >> t1 >> t2 >> t3;
adj[t1].pb({t2,t3});
adj[t2].pb({t1,t3});
}
//cari shortestpath dari u ke v
loop(i,n)dist[i] = llINF;
dist[s] = 0;
priority_queue<pllll, vector<pllll>, greater<pllll>> pq;
pq.push({0,s});
while(!pq.empty()){
ll currdist, currnode;
currdist = pq.top().first;
currnode = pq.top().second;
pq.pop();
if(currdist != dist[currnode]) continue;
for(auto edge: adj[currnode]){
ll to = edge.first;
ll c = edge.second;
if(currdist + c == dist[to]){
par[to].insert(currnode);
}
else if(currdist + c < dist[to]){
par[to].clear();
par[to].insert(currnode);
dist[to] = dist[currnode]+c;
pq.push({dist[to], to});
}
}
}
//djikstra dari u
loop(i,n)du[i] = llINF;
du[u] = 0;
// priority_queue<pllll, vector<pllll>, greater<pllll>> pq;
pq.push({0,u});
while(!pq.empty()){
ll currdist, currnode;
currdist = pq.top().first;
currnode = pq.top().second;
pq.pop();
if(currdist != du[currnode]) continue;
for(auto edge: adj[currnode]){
ll to = edge.first;
ll c = edge.second;
if(currdist + c < du[to]){
du[to] = du[currnode]+c;
pq.push({du[to], to});
}
}
}
// loop(i,n) cout << du[i] << endl;
//djikstra dari v
loop(i,n)dv[i] = llINF;
dv[v] = 0;
// priority_queue<pllll, vector<pllll>, greater<pllll>> pq;
pq.push({0,v});
while(!pq.empty()){
ll currdist, currnode;
currdist = pq.top().first;
currnode = pq.top().second;
pq.pop();
if(currdist != dv[currnode]) continue;
for(auto edge: adj[currnode]){
ll to = edge.first;
ll c = edge.second;
if(currdist + c < dv[to]){
dv[to] = dv[currnode]+c;
pq.push({dv[to], to});
}
}
}
// loop(i,n) cout << dv[i] << endl;
ans = min(ans, du[v]);
loop(i,n)d[i] = llINF;
d[t] = du[t]+dv[t];
priority_queue<pair<pllll, pllll>, vector<pair<pllll, pllll>>, greater<pair<pllll, pllll>> > q;
q.push({{du[t]+dv[t], t}, {du[t], dv[t]}});
while(!q.empty()){
ll currdist, currnode, a, b;
currdist = q.top().first.first;
currnode = q.top().first.second;
a = q.top().second.first;
b = q.top().second.second;
q.pop();
if(currdist != d[currnode]) continue;
for(auto i:par[currnode]){
ll to = i;
ll x = min(a, du[i]);
ll y = min(b, dv[i]);
if(x+y < d[to]){
d[to] = x+y;
q.push({{x+y, to},{x, y}});
}
}
}
ans = min(ans, d[s]);
cout << ans << endl;
return 0;
}
