#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
refs:
https://codeforces.com/blog/entry/68940?#comment-532790
https://codeforces.com/blog/entry/68940?#comment-532806
*/
const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
#include "split.h"
vector<int> adj1[N], adj2[N], adj3[N];
vector<bool> vis(N);
void dfs1(int u){
vis[u] = 1;
trav(v,adj1[u]){
if(vis[v]) conts;
adj2[u].pb(v), adj2[v].pb(u);
dfs1(v);
}
}
vector<int> subsiz(N);
void dfs2(int u, int p){
subsiz[u] = 1;
trav(v,adj2[u]){
if(v == p) conts;
dfs2(v,u);
subsiz[u] += subsiz[v];
}
}
int dfs3(int u, int p){
trav(v,adj2[u]){
if(v == p) conts;
if(subsiz[v] > subsiz[0]/2){
return dfs3(v,u);
}
}
return u;
}
vector<int> nodes[N];
vector<int> subr(N);
void dfs4(int u, int p, int r){
nodes[r].pb(u);
subr[u] = r;
trav(v,adj2[u]){
if(v == p) conts;
dfs4(v,u,r);
}
}
vector<int> ans;
int to_col;
void dfs5(int u, int p){
if(to_col){
ans[u] = 1;
to_col--;
}
trav(v,adj2[u]){
if(v == p) conts;
if(ans[v] != -1) conts;
dfs5(v,u);
}
}
vector<int> ord;
void dfs6(int u){
vis[u] = 1;
ord.pb(u);
trav(v,adj3[u]){
if(vis[v]) conts;
dfs6(v);
}
}
vector<int> find_split(int n, int A, int B, int C, vector<int> U, vector<int> V) {
rep(i,sz(U)){
int u = U[i], v = V[i];
adj1[u].pb(v), adj1[v].pb(u);
}
// find arbitrary spanning tree
dfs1(0);
// find centroid of spanning tree
dfs2(0,-1);
int c = dfs3(0,-1);
// root @centroid
// wlog, A <= B <= C
// if any of the subtrees have size >= A, done
// we can find a cc of size A in that subtree and this may waste at most n/2 nodes (cuz rooted @centroid)
// B <= n/2, so we can find a cc of size B in the rest of the tree
vector<int> subs;
trav(v,adj2[c]){
subs.pb(v);
dfs4(v,c,v);
}
vector<pii> col_ord = {{A,0},{B,1},{C,2}};
sort(all(col_ord));
A = col_ord[0].ff, B = col_ord[1].ff, C = col_ord[2].ff;
ans = vector<int>(n,-1);
trav(v,subs){
if(sz(nodes[v]) < A) conts;
rep(j,A){
ans[nodes[v][j]] = 0;
}
to_col = B;
dfs5(c,-1);
rep(i,n) if(ans[i] == -1) ans[i] = 2;
rep(i,n) ans[i] = col_ord[ans[i]].ss+1;
return ans;
}
// if no solution found, it means that all subtrees have size < A
// consider edges that go between subtrees
// each subtree compressed into a single node with weight = size of subtree
// add edge between 2 nodes if the corresponding subtrees are connected by an edge
// find a connected subgraph of the nodes with sum of weights >= A
// found using a dfs, stop at the first time when size >= A
// at most 2A nodes wasted after this (because all have weight < A)
// A+B+C = n, A <= C, so 2A+B <= n
// so we will be able to find a connected subgraph of size B in the remaining graph
// if no connected subgraph has sum of weights >= A, then no solution exists
rep(u,n){
trav(v,adj1[u]){
if(u == c or v == c) conts;
if(subr[u] != subr[v]){
adj3[subr[u]].pb(subr[v]);
}
}
}
fill(all(vis),0);
trav(u,subs){
if(vis[u]) conts;
ord.clear();
dfs6(u);
int sum = 0;
trav(v,ord) sum += subsiz[v];
if(sum < A) conts;
sum = 0;
trav(v,ord){
auto &curr = nodes[v];
rep(j,sz(curr)){
if(sum == A) break;
ans[curr[j]] = 0;
sum++;
}
}
assert(sum == A);
to_col = B;
dfs5(c,-1);
rep(i,n) if(ans[i] == -1) ans[i] = 2;
rep(i,n) ans[i] = col_ord[ans[i]].ss+1;
return ans;
}
fill(all(ans),0);
return ans;
}
