//Never stop trying
#include "bits/stdc++.h"
using namespace std;
#define boost ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
typedef long long ll;
#define int ll
typedef string str;
typedef long double ld;
typedef pair<int, int> pi;
#define fi first
#define se second
typedef vector<int> vi;
typedef vector<pi> vpi;
#define pb push_back
#define eb emplace_back
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define endl "\n"
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
const int MOD = 1e9 + 7; //998244353
const ll INF = 1e18;
const int MX = 2e5 + 10;
const int nx[4] = {0, 0, 1, -1}, ny[4] = {1, -1, 0, 0}; //right left down up
template<class T> bool ckmin(T& a, const T& b) { return a > b ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
ll cdiv(ll a, ll b) { return a / b + ((a ^ b) > 0 && a % b); } // divide a by b rounded up
//constexpr int log2(int x) { return 31 - __builtin_clz(x); } // floor(log2(x))
mt19937 rng(chrono::system_clock::now().time_since_epoch().count());
//mt19937_64 rng(chrono::system_clock::now().time_since_epoch().count());
ll random(ll a, ll b){
return a + rng() % (b - a + 1);
}
#ifndef LOCAL
#define cerr if(false) cerr
#endif
#define dbg(x) cerr << #x << " : " << x << endl;
#define dbgs(x,y) cerr << #x << " : " << x << " / " << #y << " : " << y << endl;
#define dbgv(v) cerr << #v << " : " << "[ "; for(auto it : v) cerr << it << ' '; cerr << ']' << endl;
#define here() cerr << "here" << endl;
void IO() {
#ifdef LOCAL
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif
}
/////////////////////////ONLY CLEAN CODES ALLOWED/////////////////////////
int N,M,S,T,U,V;
vpi adj[MX],adj2[MX];
vector<pair<pi,int>>vec; //edges
vi dist,CS(MX),CT(MX);
void sp(vpi adj[], int u){
dist.assign(N+1,INF); dist[u]=0;
priority_queue<pi,vpi,greater<pi>>q; q.push({0,u});
while(sz(q)){
int u=q.top().se,d=q.top().fi;
q.pop();
if(d>dist[u]) continue;
for(auto v: adj[u]) if(dist[v.fi]>d+v.se){
dist[v.fi]=d+v.se;
q.push({dist[v.fi],v.fi});
}
}
}
int32_t main() {
boost; IO();
cin>>N>>M>>S>>T>>U>>V;
FOR(i,0,M){
int u,v,w; cin>>u>>v>>w;
vec.pb({{u,v},w});
adj[u].pb({v,w});
adj[v].pb({u,w});
}
if(N<=300){
int g[N+1][N+1];
FOR(i,1,N+1) FOR(j,1,N+1) g[i][j]=INF;
FOR(i,1,N+1) g[i][i]=0;
for(auto x: vec){
int u=x.fi.fi,v=x.fi.se,w=x.se;
g[u][v]=g[v][u]=w;
}
FOR(k,1,N+1) FOR(i,1,N+1) FOR(j,1,N+1)
ckmin(g[i][j],g[i][k]+g[k][j]);
int ans=g[U][V];
FOR(u,1,N+1) FOR(v,1,N+1){
if(g[S][u]+g[u][v]+g[v][T]==g[S][T]){
ckmin(ans,g[U][u]+g[v][V]);
ckmin(ans,g[V][u]+g[v][U]);
}
}
cout << ans << endl;
}
else{
sp(adj,S);
FOR(i,1,N+1) CS[i]=dist[i];
sp(adj,T);
FOR(i,1,N+1) CT[i]=dist[i];
for(auto x: vec){
int u=x.fi.fi,v=x.fi.se,w=x.se;
adj2[u].pb({v,w});
adj2[v].pb({u,w});
if(CS[u]+w+CT[v]==CS[T]) adj2[u].eb(v,0);
if(CS[v]+w+CT[u]==CS[T]) adj2[v].eb(u,0);
}
sp(adj2,U);
int ans=dist[V];
FOR(i,1,N+1) adj2[i].clear();
for(auto x: vec){
int u=x.fi.fi,v=x.fi.se,w=x.se;
adj2[u].pb({v,w});
adj2[v].pb({u,w});
if(CS[u]+w+CT[v]==CS[T]) adj2[v].eb(u,0);
if(CS[v]+w+CT[u]==CS[T]) adj2[u].eb(v,0);
}
sp(adj2,U);
ckmin(ans,dist[V]);
cout << ans << endl;
}
return 0;
}
//Change your approach
