#include "split.h"
#include <bits/stdc++.h>
using namespace std;
vector<int> solve_tree(int n, array<int, 3> sc, array<int, 3> lb, vector<vector<int>> adj) {
vector<int> p(n, -1);
vector<int> sz(n, 0);
auto dfs = [&](auto&& self, int v) -> int {
sz[v] = 1;
for (int u : adj[v]) {
if (u == p[v]) continue;
p[u] = v;
sz[v] += self(self, u);
}
return sz[v];
};
dfs(dfs, rand() % n);
vector<int> ans(n, 0);
array<int, 3> cnt{};
auto colour = [&](auto&& self, int v, int c, bool risali) -> void {
if (ans[v] || cnt[c] == sc[c]) return;
ans[v] = lb[c];
++cnt[c];
for (int u : adj[v]) {
if (u == p[v] && !risali) continue;
self(self, u, c, risali);
}
};
for (int i = 0; i < n; ++i) {
for (int c = 0; c < 2; ++c) for (int d = 0; d < 2; ++d) {
if (c == d) continue;
if (sc[c] <= sz[i] && sz[i] <= sc[c] + sc[d]) {
colour(colour, i, c, false);
colour(colour, p[i], 3-c-d, true);
for (int& x : ans) if (!x) x = lb[d];
return ans;
}
}
}
return ans;
}
vector<int> find_split(int n, int a, int b, int c, vector<int> p, vector<int> q) {
array<array<int, 2>, 3> v;
v[0] = {a,1}, v[1] = {b,2}, v[2] = {c, 3};
sort(v.begin(), v.end());
array<int, 3> sc{v[0][0], v[1][0], v[2][0]};
array<int, 3> lb{v[0][1], v[1][1], v[2][1]};
vector<vector<int>> adj(n);
for (int i = 0; i < (int)p.size(); ++i) {
adj[p[i]].push_back(q[i]);
adj[q[i]].push_back(p[i]);
}
if ((int)p.size() == n - 1) {
return solve_tree(n, sc, lb, adj);
}
int min_deg = 0;
for (int i = 0; i < n; ++i) {
if (adj[i].size() < adj[min_deg].size()) {
min_deg = i;
}
}
array<int, 3> cnt{};
vector<int> ans(n, 0);
auto dfs = [&](auto&& self, int v) -> void {
if (ans[v] != 0) return;
for (int i = 0; i < 3; ++i) {
if (cnt[i] < sc[i]) {
++cnt[i];
ans[v] = lb[i];
break;
}
}
for (int u : adj[v]) {
self(self, u);
}
};
dfs(dfs, min_deg);
return ans;
}
