#include "sphinx.h"
#include <bits/stdc++.h>
using namespace std;
vector<int> find_colours(int N, vector<int> X, vector<int> Y)
{
int n = N, m = (int)X.size();
vector<int> x = X, y = Y;
vector<int> par(n), sz(n, 1);
iota(par.begin(), par.end(), 0);
auto findd = [&](auto self, int u) -> int
{
return par[u] = (par[u] == u ? u : self(self, par[u]));
};
auto unite = [&](int u, int v) -> bool
{
u = findd(findd, u);
v = findd(findd, v);
if(u == v)
return false;
if(sz[u] > sz[v])
swap(u, v);
sz[v] += sz[u];
par[u] = v;
return true;
};
vector adj(n, vector<int>());
for(int i = 0; i < m; i++)
{
adj[x[i]].push_back(y[i]);
adj[y[i]].push_back(x[i]);
}
for(int i = 0; i < n; i++)
{
int l = 0, r = adj[i].size() - 1, ans = -1;
while(l <= r)
{
int md = (l + r) / 2;
vector<int> e(n, N);
for(int j = l; j <= md; j++)
e[adj[i][j]] = -1;
int cnt = perform_experiment(e);
e[i] = -1;
int cnt2 = perform_experiment(e);
if(cnt == cnt2 and l == md)
{
unite(i, adj[i][md]);
}
if(n == 2 and cnt2 == 1)
{
unite(i, adj[i][md]);
}
if(cnt2 == cnt)
{
r = md - 1;
}
else
{
l = md + 1;
}
}
for(int j: adj[i])
adj[j].erase(find(adj[j].begin(), adj[j].end(), i));
}
set<int> st;
for(int i= 0; i < n; i++)
st.insert(findd(findd, i));
int j =0;
map<int, int> mp;
for(auto i: st)
{
mp[i] = j++;
}
vector<int> res(n);
for(int i= 0; i < n; i++)
res[i] = mp[findd(findd, i)];
return res;
}
