#include "sphinx.h"
#include <bits/stdc++.h>
using namespace std;
using vi =vector<int>;
using vvi =vector<vi>;
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define FOR(i, a, b) for (int i = a; i < b; i++)
#define all(x) (x).begin(), (x).end()
#define bg(x) (x).begin()
#define en(x) (x).end()
#define sz(x) int((x).size())
#define rev(x) reverse(all(x))
#define srt(x) sort(all(x))
#define each(a, x) for (auto &a : x)
struct DSU {
  int n; vi par, siz;
  DSU() {};
  DSU(int N) {
    n = N; siz.assign(n, 1);
    par.resize(n); iota(all(par), 0);
  } 
  int find(int v) {
    if (par[v] == v) return v;
    return par[v] = find(par[v]);
  }
  void unite(int a, int b) {
    a = find(a); b = find(b);
    if (a != b) {
      if (siz[b] > siz[a]) swap(a, b);
      par[b] = a; siz[a] += siz[b]; 
    }
  }
};
int n, m;
vi x, y;
vvi adj;
vi find_colours(int N, vi X, vi Y) {
  n = N; m = sz(X); x = X; y = Y;
  adj.assign(n, vi());
  FOR(i, 0, m) adj[x[i]].pb(y[i]), adj[y[i]].pb(x[i]);
  vi graph(n, n);
  auto dsu = DSU(n);
  int cur_colour = 0;
  FOR(i, 0, n-1) {
    int colour = graph[i] != n ? graph[i] : cur_colour++;
    vi test(n, n); test[i] = test[i+1] = -1;
    int thresh = i > 0 && i < n - 2 ? 3 : 2;
    if (perform_experiment(test) <= thresh) {
      graph[i] = graph[i+1] = colour;
    } else {
      graph[i] = colour;
    }
  }
  
  if (graph[n-1] == n) graph[n-1] = cur_colour;
  
  // FOR(i, 0, n) {
  //   FOR(col, 0, n) {
  //     vi test(n, col); test[i] = -1;
  //     if (perform_experiment(test) == 1) {
  //       graph[i] = col;
  //       // cout << "node " << i << " has colour " << col << "\n";
  //       break;
  //     }
  //   }
  // }
  return graph;
}
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