#include "split.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef double ld;
void debug_out(){cerr<<endl;}
template<typename Head, typename... Tail>
void debug_out(Head H, Tail... T){
cerr << H << ' ';
debug_out(T...);
}
#define debug(...) cerr << "(" << #__VA_ARGS__ << "): ", debug_out(__VA_ARGS__)
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define MP(x, y) make_pair(x, y)
const int maxn = 1e5 + 10;
int n, m, a, b, c, A, B, C, sz[maxn], r1 = -1, r2 = -1, ans[maxn], par[maxn];
vector<int> g[maxn], t[maxn];
bool vis[maxn];
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int getpar(int v){
return (par[v] == -1? v: par[v] = getpar(par[v]));
}
bool merge(int u, int v){
if (( u = getpar(u)) == (v = getpar(v))) return false;
par[v] = u;
return true;
}
void dfs(int v){
shuffle(all(g[v]), rng);
vector<int> save;
vis[v] = true;
for (auto u: g[v]){
if (!vis[u]){
t[u].push_back(v);
t[v].push_back(u);
int idk = rng() % 2;
if (idk) dfs(u);
else{
save.push_back(u);
vis[u] = true;
}
}
}
//if (save.empty()) return;
shuffle(all(save), rng);
for (auto u: save){
dfs(u);
}
}
void bfs(int v){
vector<int> q1;
vector<int> q2;
q1.push_back(v);
vis[v] = true;
while(!q1.empty() || !q2.empty()){
if (q1.empty()){
q1 = q2;
shuffle(all(q1), rng);
q2.clear();
}
int v = q1.back();
q1.pop_back();
for (auto u: g[v]){
if (!vis[u]){
vis[u] = true;
t[u].push_back(v);
t[v].push_back(u);
q2.push_back(u);
}
}
}
}
void find(int v, int p = -1){
sz[v] = 1;
for (auto u: t[v]){
if (u != p){
find(u, v);
sz[v] += sz[u];
}
}
if (min(n-sz[v], sz[v]) >= a){
r1 = v;
r2 = p;
}
}
int solve(int v, int p, int cnt, int val){
if (cnt == 0) return 0;
ans[v] = val;
cnt--;
for (auto u: t[v]){
if (u != p){
cnt = solve(u, v, cnt, val);
}
}
return cnt;
}
vector<int> find_split(int _n, int _a, int _b, int _c, vector<int> p, vector<int> q) {
n = _n;
m = p.size();
a = _a;
b = _b;
c = _c;
A = 1, B = 2, C = 3;
if (a > b){
swap(a, b);
swap(A, B);
}
if (b > c){
swap(b, c);
swap(B, C);
}
if (a > b){
swap(a, b);
swap(A, B);
}
vector<pii> edge;
for (int i = 0; i < m; i++){
g[p[i]].push_back(q[i]);
g[q[i]].push_back(p[i]);
edge.push_back({p[i], q[i]});
}
for (int i = 0; i < 2*n; i++){
memset(vis, false, sizeof vis);
for (int j = 0; j < n; j++) t[j].clear();
shuffle(all(edge), rng);
memset(par, -1, sizeof par);
for (auto [u, v]: edge){
if (merge(u, v)){
t[u].push_back(v);
t[v].push_back(u);
}
}
find(0);
if (r1 == -1) continue;
vector<int> res(n, C);
if (sz[r1] >= b) swap(r1, r2);
solve(r1, r2, a, A);
solve(r2, r1, b, B);
for (int i = 0; i < n; i++){
if (ans[i] != 0) res[i] = ans[i];
}
return res;
}
vector<int> res(n, 0);
return res;
}
