/**
* In the name of Allah
* We are nothing and you're everything
**/
#include <bits/stdc++.h>
#include "split.h"
using namespace std;
using ll = long long;
#define all(x) begin(x), end(x)
//#define sz(x) (int)(x).size()
const char nl = '\n';
const int N = 1e5+10;
vector<int> g[N], taze[N];
int t = 0, sz[N];
int tin[N], tout[N], cut[N], vis[N], pa[N];
vector<pair<int, int>> arr;
void dfs(int a) {
sz[a] = 1;
tin[a] = tout[a] = ++t;
for (auto i: g[a]) {
if (!tin[i]) {
dfs(i);
tout[a] = min(tout[a], tout[i]);
sz[a] += sz[i];
taze[a].push_back(i);
continue;
}
if (tin[i] == tin[a]-1)continue; // parent
tout[a] = min(tout[a], tin[i]); // back edge.
}
}
int centroid(int a, int id) {
for (auto i: taze[a]) {
if (sz[i] >= arr[id].first)return centroid(i, id);
}
return a;
}
vector<int> find_split(int n, int a, int b, int c, vector<int> p, vector<int> q) {
int m = (int)p.size();
arr.push_back({a, 1});
arr.push_back({b, 2});
arr.push_back({c, 3});
for (int i = 0; i < m; ++i) {
int u = p[i], v = q[i];
g[u].push_back(v);
g[v].push_back(u);
}
sort(all(arr));
vector<int> ans(n, arr[2].second);
dfs(0);
int v = centroid(0, 0);
function<void(int, int)> one = [&](int u, int par) {
if (!arr[1].first)return;
arr[1].first -= 1;
ans[u] = arr[1].second;
vis[u] = 1;
for (auto i: g[u]) {
if (vis[i] == 1)continue;
one(i, u);
}
};
function<void(int, int)> zero = [&](int u, int par) {
if (arr[0].first) {
arr[0].first -= 1;
ans[u] = arr[0].second;
}
vis[u] = 1;
for (auto i: taze[u]) {
//if (vis[i] == 1 || cut[i] == 1)continue;
zero(i, u);
}
};
int sum = 0;
for (auto i: taze[v]) {
if (tout[i] < tin[v]) {
if (sz[v]-sum-sz[i] >= arr[0].first) {
sum += sz[i];
cut[i] = 1;
}
}
}
if (n-sz[v] >= arr[1].first) {
arr[0].first -= 1;
ans[v] = arr[0].second;
vis[v] = 1;
for (auto i: taze[v]) {
if (!cut[i])zero(i, i);
}
bool ok = true;
for (int i = 0; i < n; ++i) {
if (vis[i] == 0) {
one(i, i);
ok = false;
break;
}
}
if (arr[0].first != 0 || arr[1].first != 0)ok = true;
if (!ok)
return ans;
}
for (int i = 0; i < n; ++i) {
cut[i] = vis[i] = 0;
ans[i] = arr[2].second;
}
v = centroid(0, 1);
sum = 0;
for (auto i: taze[v]) {
if (tout[i] < tin[v]) {
if (sz[v]-sum-sz[i] >= arr[1].first) {
sum += sz[i];
cut[i] = 1;
}
}
}
swap(arr[0], arr[1]);
if (n-sz[v] >= arr[1].first) {
arr[0].first -= 1;
ans[v] = arr[0].second;
vis[v] = 1;
for (auto i: taze[v]) {
if (!cut[i])zero(i, i);
}
bool ok = true;
for (int i = 0; i < n; ++i) {
if (vis[i] == 0) {
one(i, i);
break;
}
}
if (arr[0].first != 0 || arr[1].first != 0)ok = true;
return ans;
}
return vector<int>(n, 0);
}
//void solve() {
//vector<int> ans = find_split(9, 4, 2, 3, {0, 0, 0, 0, 0, 0, 1, 3, 4, 5}, {1, 2, 3, 4, 6, 8, 7, 7, 5, 6});
//for (auto i: ans)cout << i << " ";
//}
//int32_t main() {
//ios::sync_with_stdio(0);
//cin.tie(0);
//solve();
//return 0;
//}
