#include "split.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ld double
#define sz(x) (int)x.size()
#define all(x) x.begin(),x.end()
#define pb emplace_back
#define X first
#define Y second
typedef pair<int,int> ii;
const int N = 2e5 + 5;
int p[N];
int s[N];
int init(int n) {
iota(p,p + n,0);
fill(s,s + n,1);
return 1;
}
int lead(int x) { return p[x] == x ? x : p[x] = lead(p[x]); }
int join(int x,int y) {
x = lead(x);
y = lead(y);
if (x == y) return 0;
if (s[x] < s[y])
swap(x,y);
p[y] = x;
s[x] += s[y];
return 1;
}
bool sameSet(int x,int y) {
x = lead(x);
y = lead(y);
return x == y;
}
typedef vector<int> vec;
int findRoot(int mxSize,const vector<vec> &adj) {
vector<int> s(sz(adj),0);
vector<int> p(sz(adj),-1);
function<void(int)> dfs = [&](int u) {
s[u] = 1;
for(int v : adj[u]) if (v != p[u]) {
p[v] = u; dfs(v);
s[u] += s[v];
}
};
dfs(0);
for(int u = 0 ;;) {
int siz = -1;
int idx = 0;
for(int v : adj[u]) if (v != p[u])
if (siz < s[v])
siz = s[v],
idx = v;
if (siz <= mxSize) return u;
u = idx;
}
}
vector<int> find_split(int n,int a,int b,int c,vector<int> p,vector<int> q) {
vector<int> res(n,0);
vector<ii> color_Set;
color_Set.pb(a,1);
color_Set.pb(b,2);
color_Set.pb(c,3);
sort(all(color_Set));
a = color_Set[0].X; int ca = color_Set[0].Y;
b = color_Set[1].X; int cb = color_Set[1].Y;
c = color_Set[2].X; int cc = color_Set[2].Y;
vector<vec> g(n);
init(n);
for(int i = 0 ; i < sz(p) ; ++i)
if (join(p[i],q[i])) {
g[p[i]].pb(q[i]);
g[q[i]].pb(p[i]);
}
init(n);
int r = findRoot(n - b,g);
for(int i = 0 ; i < n ; ++i)
for(int x : g[i]) {
if (i == r) continue;
if (x == r) continue;
join(i,x);
}
for(int i = 0 ; i < sz(p) ; ++i) {
int x = p[i];
int y = q[i];
if (sameSet(x,y)) continue;
if (x == r) continue;
if (y == r) continue;
if (s[lead(x)] >= a) continue;
if (s[lead(y)] >= a) continue;
join(x,y);
g[x].pb(y);
g[y].pb(x);
}
function<void(int,int&,int,int)> cal = [&](int u,int&n,int c,int bad) {
if (u == bad) return;
if (res[u]) return;
if (n == 0) return;
res[u] = c;
n--;
for(int v : g[u])
cal(v,n,c,bad);
};
for(int v : g[r]) if (s[lead(v)] >= a) {
cal(v,a,ca,r);
cal(r,b,cb,-1); // color root and its surrounding subgraph for set B
replace(all(res),0,cc);
break;
}
return res;
}
