#include "split.h"
#include<bits/stdc++.h>
using namespace std;
#define ll long long int
#define pb push_back
#define ff first
#define all(x) x.begin(), x.end()
#define ss second
const int N = 5e5;
int n;
vector<int> g[N];
vector<int> res;
vector<bool> vis;
vector<vector<bool>> edge;
int par[N];
void fill(int v, int par, int col, int &colnum){
queue<int> q;
q.push(v);
vis[v] = 1;
vis[par] = 1;
res[v] = col;
--colnum;
while(!q.empty()){
int v = q.front();
q.pop();
// cout << v << ' ' << a << ' ' << b << ' ' << c << '\n';
for(int u: g[v]){
if(!vis[u]){
if(colnum > 0 && (n >= 3000 || edge[u][v])){
res[u] = col;
--colnum;
// cout << v << ' ' << 2 << '\n';
}else break;
vis[u] = 1;
q.push(u);
}
}
if(colnum == 0) break;
}
vis[par] = 0;
}
vector<bool> viss;
int sz[N], tin[N], tout[N], timer = 0;
void dfs(int v, int p){
sz[v] = 1;
par[v] = p;
tin[v] = timer++;
viss[v] = 1;
for(int u: g[v]){
if(u != p && !viss[u]){
if(n < 3000){
edge[u][v] = edge[v][u] = 1;
}
dfs(u, v);
sz[v] += sz[u];
}
}
tout[v] = timer++;
}
bool is_ancestor(int u, int v){
return tin[u] <= tin[v] && tout[v] <= tout[u];
}
vector<int> find_split(int nn, int a, int b, int c, vector<int> Y, vector<int> X) {
n = nn;
vector<pair<int, int>> arr;
arr.pb({a, 1});
arr.pb({b, 2});
arr.pb({c, 3});
sort(all(arr));
for(int i = 1; i < Y.size(); ++i){
int r = rand() % i;
swap(Y[i], Y[r]);
swap(X[i], X[r]);
}
for(int i = 0; i < Y.size(); ++i){
g[Y[i]].pb(X[i]);
g[X[i]].pb(Y[i]);
}
if(n < 3000){
int root = 0;
edge.resize(n, vector<bool>(n));
res.clear();
res.resize(n+1);
vis.clear();
vis.resize(n+1);
viss.clear();
viss.resize(n+1);
dfs(root, n);
bool ok = 0;
int A = 0;
for(int i = 0; i < n; ++i){
if(i == root) continue;
if(sz[i] >= arr[0].ff && sz[root] - sz[i] >= arr[1].ff){
fill(i, par[i], arr[0].ss, arr[0].ff);
fill(root, par[root], arr[1].ss, arr[1].ff);
ok = 1;
break;
}else if(sz[i] >= arr[1].ff && sz[root] - sz[i] >= arr[0].ff){
fill(i, par[i], arr[1].ss, arr[1].ff);
fill(root, par[root], arr[0].ss, arr[0].ff);
ok = 1;
break;
}
if(sz[i] >= arr[0].ff) A = 1;
}
if(!ok && A == 0){
res.pop_back();
return res;
}
if(ok){
res.pop_back();
for(int &cc: res) if(cc == 0) cc = arr[2].ss;
return res;
}
for(int v = 1; v < n; ++v){
if(sz[v] >= arr[0].ff){ // v kotu node
vector<pair<int, int>> good;
int tot = 0;
for(int u = 1; u < n; ++u){
if(is_ancestor(v, u) && u != v && sz[u] < arr[0].ff && sz[par[u]] >= arr[0].ff){ // kendi iyi, parenti kotu
bool k = 0;
for(int j: g[u]){
if(is_ancestor(v, j) == 0) k = 1;
}
if(k){
good.pb({sz[u], u});
tot += sz[u];
}
}
}
if(sz[root] - (sz[v] - tot) >= arr[0].ff){
sort(all(good));
vector<int> U;
for(auto p: good){
if(sz[root] - sz[v] < arr[0].ff){
sz[v] -= p.ff;
U.pb(p.ss);
}else break;
}
if(sz[root] - sz[v] >= arr[0].ff && sz[v] >= arr[1].ff){
for(int u: U){
fill(u, par[u], arr[0].ss, arr[0].ff);
}
fill(v, par[v], arr[1].ss, arr[1].ff);
fill(root, par[root], arr[0].ss, arr[0].ff);
}else{
for(int u: U){
fill(u, par[u], arr[1].ss, arr[1].ff);
}
fill(v, par[v], arr[0].ss, arr[0].ff);
fill(root, par[root], arr[1].ss, arr[1].ff);
}
ok = 1;
break;
}
}
}
if(!ok){
res.pop_back();
return res;
}
res.pop_back();
for(int &cc: res) if(cc == 0) cc = arr[2].ss;
return res;
}
for(int root = 0; root < n; ++root){
res.clear();
res.resize(n+1);
vis.clear();
vis.resize(n+1);
viss.clear();
viss.resize(n+1);
dfs(root, n);
bool ok = 0;
for(int i = 0; i < n; ++i){
if(i == root) continue;
if(sz[i] >= arr[0].ff && sz[root] - sz[i] >= arr[1].ff){
fill(i, par[i], arr[0].ss, arr[0].ff);
fill(root, par[root], arr[1].ss, arr[1].ff);
ok = 1;
break;
}else if(sz[i] >= arr[1].ff && sz[root] - sz[i] >= arr[0].ff){
fill(i, par[i], arr[1].ss, arr[1].ff);
fill(root, par[root], arr[0].ss, arr[0].ff);
ok = 1;
break;
}
}
if(!ok){
if(X.size() == nn-1) break;
continue;
}
res.pop_back();
for(int &cc: res) if(cc == 0) cc = arr[2].ss;
return res;
}
res.pop_back();
return res;
}
