#include <bits/stdc++.h>
#include "split.h"
#ifndef EVAL
#include "grader.cpp"
#endif
using namespace std;
#define ff first
#define ss second
#define pb push_back
#define mp make_pair
#define ub upper_bound
#define lb lower_bound
#define ll long long
#define ld long double
#define pii pair<int, int>
#define pll pair<ll, ll>
#define sz(x) (int)x.size()
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(),x.rend()
#define fastios ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define vll vector<ll>
#define vii vector<int>
#define vpii vector<pii>
#define vpll vector<pll>
#define cnt(a)__builtin_popcount(a)
template<class T> bool umin(T& a, const T& b) {return a > b? a = b, true:false;}
template<class T> bool umax(T& a, const T& b) {return a < b? a = b, true:false;}
using namespace std;
const int N = 2e5+5;
vpii dd, ex;
vii edges[N];
int par[N], sz[N], sis[N];
int nn, rr;
void dfs(int u, int p){
sis[u] = 1;
for(auto x:edges[u]){
if(x == p) continue;
dfs(x, u);
sis[u] += sis[x];
}
}
int dfs_centr(int u, int p){
int mx = 0, in = -1;
for(auto x:edges[u]){
if(x == p) continue;
if(sis[x] > mx) mx = sis[x], in = x;
}
assert(in != -1);
if(mx*2 > nn) return dfs_centr(in, u);
return u;
}
/* ###############################################################################
* dsu part
* ############################################################################### */
int f(int x){
if(x == par[x]) return x;
return par[x] = f(par[x]);
}
void merge(int a, int b){
a = f(a), b = f(b);
par[b] = a;
sz[a] += sz[b];
}
void add_dsu(int u, int p){
for(auto x:edges[u]){
if(x == p) continue;
merge(u, x);
add_dsu(x, u);
}
}
/* ###############################################################################
* solving part
* ############################################################################### */
set<pii> ss;
bool check(){
if(!sz(ss)) return 0;
auto x = --ss.end();
return (*x).ff >= dd[0].ff;
}
vector<int> res;
int siz;
void s_a(int u){
res[u] = dd[0].ss, siz++;
if(siz == dd[0].ff) return;
for(auto x:edges[u]){
if(f(x) != f(u)) continue;
s_a(x);
if(siz == dd[0].ff) return;
}
}
void s_b(int u){
res[u] = dd[1].ss, siz++;
if(siz == dd[1].ff) return;
for(auto x:edges[u]){
if(res[x]) continue;
s_b(x);
if(siz == dd[1].ff) return;
}
}
vector<int> solve(){
res.clear();
siz = 0;
res.assign(nn, 0);
s_a((*--ss.end()).ss);
assert(siz == dd[0].ff);
siz = 0;
s_b(rr);
assert(siz == dd[1].ff);
siz = 0;
for(int i=0;i<nn;i++) if(res[i] == 0) res[i] = dd[2].ss, siz++;
assert(siz == dd[2].ff);
return res;
}
/* ###############################################################################
* end of solving part
* ############################################################################### */
vector<int> find_split(int n, int a, int b, int c, vector<int> p, vector<int> q) {
nn = n;
dd.pb(mp(a, 1));
dd.pb(mp(b, 2));
dd.pb(mp(c, 3));
sort(all(dd));
for(int i=0;i<n;i++) par[i] = i, sz[i] = 1;
for(int i=0;i<sz(p);i++){
int a = p[i], b = q[i];
int pa = f(a), pb = f(b);
if(pa == pb) ex.pb({a, b});
else{
merge(pa, pb);
edges[a].pb(b);
edges[b].pb(a);
}
}
//cout<<"passed";
dfs(0, -1);
rr = dfs_centr(0, -1);
for(int i=0;i<n;i++) par[i] = i, sz[i] = 1;
for(auto x:edges[rr]){
add_dsu(x, rr);
ss.insert(mp(sz[x], f(x)));
}
//cout<<"\n";
//for(auto x:ss) cout<<x.ff<<" "<<x.ss<<"\n";
if(check()) return solve();
for(auto x : ex){
if(x.ff == rr || x.ss == rr) continue;
int pa = f(x.ff), pb = f(x.ss);
if(pa == pb) continue;
ss.erase({sz[pa], pa});
ss.erase({sz[pb], pb});
merge(pa, pb);
ss.insert({sz[pa], pa});
if(check()) return solve();
}
res.assign(n, 0);
return res;
}
/*
6 5
2 2 2
0 1
0 2
0 3
0 4
0 5
9 11 2 3 4
0 1
0 2
0 4
0 3
0 5
0 6
0 8
1 7
3 7
4 5
5 6
*/
