#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pii;
#define mp make_pair
#define pb push_back
#define F first
#define S second
#define debug(x) std::cout << #x << ": " << x << "\n"
#define all(v) v.begin(), v.end()
#define li(i,a,b) for (int (i) = (a); (i) < (b); (i)++)
#define endl '\n'
#define mem(name,val) memset(name,val,sizeof(name))
#define min(a,b) (a<=b ? a : b)
#define max(a,b) (a>=b ? a : b)
//using u64 = uint64_t;
//using u128 = __uint128_t;
const int nmax = 1e5+3;
const ll inf = 1e18;
vector<pii> adj[nmax];
vector<int> bes[nmax], invbes[nmax];
bool vis[nmax],best[nmax];
void dijk(vector<ll> &d, int s){
priority_queue<pii, vector<pii>, greater<pii>> pq;
d[s]=0;
pq.push({0,s});
while(!pq.empty()){
const auto [d_v, v] = pq.top();
pq.pop();
if(d_v!=d[v]) continue;
for(const auto [to, len] : adj[v]){
if(d_v+len<d[to]){
d[to] = d_v+len;
pq.push({d[to],to});
}
}
}
}
void dijk2(vector<ll> &d, int s){
priority_queue<pii, vector<pii>, greater<pii>> pq;
d[s]=0;
pq.push({0,s});
while(!pq.empty()){
const auto [d_v, v] = pq.top();
pq.pop();
if(d_v!=d[v] || best[v]) continue;
for(const auto [to, len] : adj[v]){
if(d_v+len<d[to]){
d[to] = d_v+len;
pq.push({d[to],to});
}
}
}
}
void dfs(int u, vector<ll> &d){
vis[u] = 1;
for(const auto [to, len]:adj[u]){
if(d[to]+len==d[u]){
best[to]=1;
bes[u].pb(to);
invbes[to].pb(u);
}
if(!vis[to])dfs(to,d);
}
}
void topodfs(int u, vector<int> &po, vector<int> graph[]){
vis[u] = 1;
for(int v:graph[u]){
if(!vis[v])topodfs(v,po,graph);
}
po.pb(u);
}
int main()
{
ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
int n,m,s,t,u,v,a,b,c;
cin>>n>>m>>s>>t>>u>>v;
li(i,0,m){
cin>>a>>b>>c;
adj[a].pb({b,c});
adj[b].pb({a,c});
}
vector<ll> ds(nmax, inf), du(nmax, inf), dv(nmax, inf), minv(nmax, inf), dp1(nmax,inf), dp2(nmax, inf);
dijk(ds,s);
mem(vis,0); mem(best,0);
best[t]=1;
dfs(t,ds);
dijk(du,u);
dijk(dv,v);
//topo sort
vector<int> ts;
mem(vis,0);
topodfs(t,ts,bes);
reverse(all(ts));
for(int g : ts){
dp1[g] = dv[g];
for(int gk : invbes[g]){
dp1[g] = min(dp1[g], dp1[gk]);
}
}
vector<int> ts2;
mem(vis,0);
topodfs(s,ts2,invbes);
reverse(all(ts2));
for(int g : ts2){
dp2[g] = dv[g];
for(int gk : bes[g]){
dp2[g] = min(dp2[g], dp2[gk]);
}
}
// end game
ll res = dv[u];
for(int g : ts){
res = min(res, du[g] + min(dp1[g],dp2[g]));
}
cout<<res;
return 0;
}
