// I can do all things through Christ who strengthens me
// Philippians 4:13
#include "split.h"
#include "bits/stdc++.h"
using namespace std;
#define REP(i, j, k) for (int i = j; i < (k); i++)
#define RREP(i, j, k) for (int i = j; i >= (k); i--)
template <class T>
inline bool mnto(T &a, const T b) {return a > b ? a = b, 1 : 0;}
template <class T>
inline bool mxto(T &a, const T b) {return a < b ? a = b, 1 : 0;}
typedef long long ll;
typedef long double ld;
#define FI first
#define SE second
typedef pair<int, int> ii;
typedef pair<ll, ll> pll;
#define SZ(x) (int) x.size()
#define ALL(x) x.begin(), x.end()
#define pb push_back
typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<ll> vll;
typedef tuple<int, int, int> iii;
typedef vector<iii> viii;
#ifndef DEBUG
#define cerr if (0) cerr
#endif
const int INF = 1000000005;
const ll LINF = 1000000000000000005;
const int MAXN = 200005;
int n, m, s[3], ss[3];
vi adj[MAXN];
vi ans;
bool ban[MAXN];
vi tree[MAXN];
void mark(int u, int p, int &rem, int x) {
if (rem == 0) {
return;
}
ans[u] = x;
rem--;
for (int v : tree[u]) {
if (v == p || ban[v]) {
continue;
}
mark(v, u, rem, x);
}
}
void markall(int u, int &rem, int x) {
if (rem == 0) {
return;
}
ans[u] = x;
rem--;
for (int v : adj[u]) {
if (ans[v] != 3) {
continue;
}
markall(v, rem, x);
}
}
int sub[MAXN];
int pre[MAXN], low[MAXN], ptr;
void getsub(int u, int p) {
sub[u] = 1;
pre[u] = low[u] = ptr++;
for (int v : adj[u]) {
if (v == p) {
continue;
}
if (pre[v] != -1) {
mnto(low[u], pre[v]);
continue;
}
tree[u].pb(v);
tree[v].pb(u);
getsub(v, u);
mnto(low[u], low[v]);
sub[u] += sub[v];
}
}
bool dfs(int u, int p) {
bool bad = sub[u] < s[ss[0]] || u == 0;
for (int v : tree[u]) {
if (v == p) {
continue;
}
if (sub[v] >= s[ss[0]] && n - sub[v] >= s[ss[1]]) {
mark(v, u, s[ss[0]], ss[0] + 1);
mark(u, v, s[ss[1]], ss[1] + 1);
return 1;
}
bad |= sub[v] >= s[ss[0]];
if (dfs(v, u)) {
return 1;
}
}
if (bad) {
return 0;
}
assert(sub[u] > s[ss[0]] + s[ss[2]]);
int csub = sub[u];
ban[p] = 1;
cerr << u << '\n';
cerr << ' ' << p << '\n';
for (int v : tree[u]) {
if (v == p) {
continue;
}
if (low[v] < pre[u]) {
cerr << ' ' << v << '\n';
ban[v] = 1;
csub -= sub[v];
if (csub >= s[ss[0]] && n - csub >= s[ss[1]]) {
mark(u, p, s[ss[0]], ss[0] + 1);
markall(p, s[ss[1]], ss[1] + 1);
assert(s[ss[1]] <= 0);
return 1;
}
}
}
for (int v : tree[u]) {
ban[v] = 0;
}
return 0;
}
vi find_split(int n, int a, int b, int c, vi p, vi q) {
::n = n; s[0] = a; s[1] = b; s[2] = c;
iota(ss, ss + 3, 0);
sort(ss, ss + 3, [&] (int l, int r) {
return s[l] < s[r];
});
m = SZ(p);
REP (i, 0, m) {
adj[p[i]].pb(q[i]);
adj[q[i]].pb(p[i]);
}
ans = vi(n, ss[2] + 1);
memset(pre, -1, sizeof pre);
getsub(0, -1);
if (dfs(0, -1)) {
return ans;
}
swap(ss[0], ss[1]);
if (dfs(0, -1)) {
return ans;
}
ans = vi(n, 0);
return ans;
}
