#include "split.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
struct DSU{
int path[100100];
void init(int n){for (int i=0;i<n;i++) path[i] = i;}
int find(int s){
if (s==path[s]) return s;
return path[s] = find(path[s]);
}
bool merge(int s, int v){
s = find(s), v = find(v);
if (s==v) return 0;
path[s] = v;
return 1;
}
}dsu;
int n, a, b, c, sz[100100], par[100100], idx[5];
void dfs(int s, int &cnt, int no, const vector<vector<int>> &adj, int num, vector<int> &ret){
if (!cnt) return;
--cnt;
ret[s] = num;
if (no==-1) sz[s] = 1;
for (auto &v:adj[s]) if (v!=no && ret[v]!=num){
if (no==-1) par[v] = s;
dfs(v, cnt, no, adj, num, ret);
if (no==-1) sz[s] += sz[v];
}
}
vector<int> solve_tree(const vector<vector<int>> &adj){
vector<int> ret(n);
int N = n;
dfs(0, N, -1, adj, idx[3], ret);
for (int i=1;i<n;i++){
int x = sz[i], y = n - sz[i];
if (a<=x && b<=y){
dfs(i, a, par[i], adj, idx[1], ret);
dfs(par[i], b, i, adj, idx[2], ret);
return ret;
}
if (a<=y && b<=x){
dfs(par[i], a, i, adj, idx[1], ret);
dfs(i, b, par[i], adj, idx[2], ret);
return ret;
}
}
fill(ret.begin(), ret.end(), 0);
return ret;
}
int dist[100100], bp[100100], de = -1, dval = -1;
void bfs(int s, const vector<vector<int>> &adj){
bp[s] = -1;
fill(dist, dist+n, 1e9);
dist[s] = 0;
queue<int> q;
q.push(s);
while(!q.empty()){
int cur = q.front(); q.pop();
for (auto &v:adj[cur]) if (dist[v]==1e9){
dist[v] = dist[cur] + 1;
bp[v] = cur;
q.push(v);
}
}
int mx = *max_element(dist, dist+n);
if (dval<mx) de = s, dval = mx;
}
vector<int> find_split(int N, int A, int B, int C, vector<int> p, vector<int> q) {
n = N;
vector<pair<int, int>> tmp;
tmp.emplace_back(A, 1);
tmp.emplace_back(B, 2);
tmp.emplace_back(C, 3);
sort(tmp.begin(), tmp.end());
a = tmp[0].first, b = tmp[1].first, c = tmp[2].first;
idx[1] = tmp[0].second, idx[2] = tmp[1].second, idx[3] = tmp[2].second;
vector<vector<int>> adj0(N, vector<int>());
for (int i=0;i<(int)p.size();i++){
adj0[p[i]].push_back(q[i]);
adj0[q[i]].push_back(p[i]);
}
vector<vector<int>> adj(n);
dsu.init(n);
for (int i=0;i<n;i++) bfs(i, adj0);
bfs(de, adj0);
int de2 = max_element(dist, dist+n) - dist;
while(bp[de2]!=-1){
adj[de2].push_back(bp[de2]);
adj[bp[de2]].push_back(de2);
dsu.merge(de2, bp[de2]);
de2 = bp[de2];
}
for (int i=0;i<(int)p.size();i++) if (dsu.merge(p[i], q[i])){
adj[p[i]].push_back(q[i]);
adj[q[i]].push_back(p[i]);
}
return solve_tree(adj);
}
