#include "split.h"
#include <bits/stdc++.h>
using namespace std;
#define sz(v) int(v.size())
#define ar array
typedef long long ll;
const int N = 2e5+10, MOD = 1e9+7;
struct DSU {
vector<int> par, sz;
DSU() {}
DSU(int n): par(n) {
iota(par.begin(), par.end(), 0);
sz.assign(n, 1);
}
int find_set(int v) {
return v == par[v] ? v : par[v] = find_set(par[v]);
}
bool union_sets(int a, int b) {
if ((a = find_set(a)) == (b = find_set(b))) return false;
if (sz[a] < sz[b]) swap(a, b);
par[b] = a, sz[a] += sz[b], sz[b] = 0;
return true;
}
} d;
int n, m, sub[N], who[N];
vector<int> adj[N];
vector<int> tree[N], extra[N];
bool vis[N];
void dfs_tree(int c) {
vis[c] = 1;
for (int nxt : adj[c]) if (!vis[nxt]) {
tree[c].push_back(nxt);
tree[nxt].push_back(c);
dfs_tree(nxt);
}
}
int dfs_sub(int c, int p) {
sub[c] = 1;
for (int nxt : tree[c]) if (nxt != p) {
sub[c] += dfs_sub(nxt, c);
}
return sub[c];
}
int dfs_cent(int c, int p) {
for (int nxt : tree[c]) if (nxt != p && sub[nxt] > n / 2)
return dfs_cent(nxt, c);
return c;
}
void dfs_who(int c, int p, int cur) {
who[c] = cur;
for (int nxt : tree[c]) if (nxt != p) {
dfs_who(nxt, c, cur);
}
}
bool marked[N];
void dfs_mark(int c, int p) {
marked[c] = 1;
for (int nxt : tree[c]) if (nxt != p) {
dfs_mark(nxt, c);
}
}
vector<int> collect;
int sum = 0;
void dfs_collect(int c) {
vis[c] = 1;
if (sum > 0) {
sum -= sub[c];
collect.push_back(c);
}
for (int nxt : extra[c]) if (!vis[nxt]) {
dfs_collect(nxt);
}
}
vector<int> ord;
bool only[N], has[N];
void dfs_ord(int c) {
has[c] = 1;
ord.push_back(c);
for (int nxt : adj[c]) if (!has[nxt] && only[nxt]) {
dfs_ord(nxt);
}
}
vector<int> trim(vector<int> nodes, int cnt) {
memset(only, 0, sizeof(only));
memset(has, 0, sizeof(has));
for (int x : nodes) only[x] = 1;
ord.clear();
dfs_ord(nodes[0]);
ord.resize(cnt);
return ord;
}
vector<int> get_from_mark(const vector<pair<int, int>>& cols) {
vector<int> one, two;
for (int i = 0; i < n; i++) {
if (marked[i]) one.push_back(i);
else two.push_back(i);
}
one = trim(one, cols[0].first);
two = trim(two, cols[1].first);
vector<int> ans(n, cols[2].second);
for (int x : one) ans[x] = cols[0].second;
for (int x : two) ans[x] = cols[1].second;
return ans;
}
vector<int> find_split(int _n, int p1, int p2, int p3, vector<int> p, vector<int> q) {
n = _n, m = sz(p);
for (int i = 0; i < m; i++) {
int x = p[i], y = q[i];
adj[x].push_back(y), adj[y].push_back(x);
}
vector<pair<int, int>> cols(3);
cols[0] = {p1, 1}, cols[1] = {p2, 2}, cols[2] = {p3, 3};
sort(cols.begin(), cols.end());
dfs_tree(0);
dfs_sub(0, -1);
int root = dfs_cent(0, -1);
dfs_sub(root, -1);
who[root] = -1;
for (int nxt : tree[root]) {
dfs_who(nxt, root, nxt);
}
for (int nxt : tree[root]) {
if (sub[nxt] >= cols[0].first) {
dfs_mark(nxt, root);
return get_from_mark(cols);
}
}
for (int i = 0; i < m; i++) {
if (who[p[i]] != who[q[i]] && who[p[i]] >= 0 && who[q[i]] >= 0) {
extra[who[p[i]]].push_back(who[q[i]]);
extra[who[q[i]]].push_back(who[p[i]]);
}
}
memset(vis, 0, sizeof(vis));
for (int nxt : tree[root]) if (!vis[nxt]) {
collect.clear();
sum = cols[0].first;
dfs_collect(nxt);
if (sum > 0) continue;
for (int v : collect) dfs_mark(v, root);
return get_from_mark(cols);
}
return vector<int>(n, 0);
}
