#include "sphinx.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
struct DSU{
int path[2020], col[2020];
void init(int n){
for (int i=0;i<n;i++) path[i] = i, col[i] = i + 2020;
}
int find(int s){
if (s==path[s]) return s;
return path[s] = find(path[s]);
}
int merge(int x, int y){
x = find(x), y = find(y);
if (x==y) return 0;
path[x] = y;
return 1;
}
int getcol(int s){return col[find(s)];}
void setcol(int s, int c){col[find(s)] = c;}
}dsu, dsu2;
int N, tmp;
vector<int> X, Y;
int predict(vector<int> Q){
int ret = N;
dsu2.init(N);
for (int i=0;i<(int)X.size();i++){
int cx = Q[X[i]], cy = Q[Y[i]];
if (cx == -1) cx = dsu.getcol(X[i]);
if (cy == -1) cy = dsu.getcol(Y[i]);
if (cx == cy) ret -= dsu2.merge(X[i], Y[i]);
}
return ret;
}
int query(vector<int> Q, bool flag = false){
int ret = predict(Q);
if (flag){
tmp = perform_experiment(Q);
ret -= tmp;
}
else ret -= perform_experiment(Q);
assert(ret >= 0);
return ret;
}
std::vector<int> find_colours(int N, std::vector<int> X, std::vector<int> Y) {
::N = N, ::X = X, ::Y = Y;
dsu.init(N);
// phase 1 (50 points)
for (int i=0;i<N;i++){
vector<int> Q(N, N);
for (int j=0;j<=i;j++) Q[j] = -1;
int t = query(Q);
while(t--){
vector<int> adj;
for (int j=0;j<(int)X.size();j++){
int x = dsu.find(X[j]), y = dsu.find(Y[j]);
if (x == y) continue;
if (x == dsu.find(i) && y < i) adj.push_back(y);
if (x < i && y == dsu.find(i)) adj.push_back(x);
}
sort(adj.begin(), adj.end());
adj.erase(unique(adj.begin(), adj.end()), adj.end());
int l = 0, r = (int)adj.size() - 1, v = (int)adj.size();
while(l<=r){
int mid = (l+r)>>1;
vector<int> Q(N, N);
for (int j=0;j<N;j++){
if (dsu.find(j) == dsu.find(i)) Q[j] = -1;
if (find(adj.begin(), adj.end(), dsu.find(j)) - adj.begin() <= mid) Q[j] = -1;
}
if (query(Q) > 0) r = mid-1, v = mid;
else l = mid+1;
}
if (v == (int)adj.size()){
if (query(Q) == 0) return {};
}
assert(v < (int)adj.size());
dsu.merge(i, adj[v]);
}
}
// phase 2
vector<vector<int>> adj(N), buf(2);
vector<int> typ(N, -1);
for (int i=0;i<(int)X.size();i++){
adj[dsu.find(X[i])].push_back(dsu.find(Y[i]));
adj[dsu.find(Y[i])].push_back(dsu.find(X[i]));
}
auto dfs = [&](auto self, int s, int c) -> void {
typ[s] = c;
buf[c].push_back(s);
for (auto &v:adj[s]) if (typ[v] == -1) self(self, v, c^1);
};
dfs(dfs, dsu.find(0), 0);
for (int z=0;z<2;z++){
for (int c=0;c<N;c++){
vector<int> Q(N, -1);
for (int i=0;i<N;i++) if (typ[dsu.find(i)] != z) Q[i] = c;
query(Q, true);
while(true){
fill(Q.begin(), Q.end(), -1);
for (int i=0;i<N;i++) if (typ[dsu.find(i)] != z) Q[i] = c;
if (tmp == predict(Q)) break;
int l = 0, r = (int)buf[z].size() - 1, v = (int)buf[z].size();
while(l <= r){
int mid = (l+r)>>1;
for (int i=0;i<N;i++) if (typ[dsu.find(i)] == z){
if (find(buf[z].begin(), buf[z].end(), dsu.find(i)) - buf[z].begin() <= mid) Q[i] = -1;
else Q[i] = N;
}
if (query(Q) > 0) r = mid-1, v = mid;
else l = mid+1;
}
assert(v < (int)buf[z].size());
dsu.setcol(buf[z][v], c);
}
}
}
vector<int> ret(N);
for (int i=0;i<N;i++) ret[i] = dsu.getcol(i);
return ret;
}
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