#ifndef hwe
#include "sphinx.h"
#endif
#include <bits/stdc++.h>
using namespace std;
#define popcount(n) (__builtin_popcountll((n)))
#define clz(n) (__builtin_clzll((n)))
#define ctz(n) (__builtin_ctzll((n)))
#define lg(n) (63 - __builtin_clzll((n)))
#define BIT(n, i) (((n) >> (i)) & 1ll)
#define MASK(i) (1ll << (i))
#define FLIP(n, i) ((n) ^ (1ll << (i)))
#define ON(n, i) ((n) | MASK(i))
#define OFF(n, i) ((n) & ~MASK(i))
#define Int __int128
#define fi first
#define se second
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
typedef pair<long long, int> pli;
typedef pair<int, long long> pil;
typedef vector<pair<int, int>> vii;
typedef vector<pair<long long, long long>> vll;
typedef vector<pair<long long, int>> vli;
typedef vector<pair<int, long long>> vil;
template <class T1, class T2>
bool maximize(T1 &x, T2 y) {
if (x < y) {
x = y;
return true;
}
return false;
}
template <class T1, class T2>
bool minimize(T1 &x, T2 y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <class T>
void remove_duplicate(vector<T> &ve) {
sort (ve.begin(), ve.end());
ve.resize(unique(ve.begin(), ve.end()) - ve.begin());
}
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
template <class T> T random(T l, T r) {
return uniform_int_distribution<T>(l, r)(rng);
}
template <class T> T random(T r) {
return rng() % r;
}
const int N = 250 + 5;
const int MOD = 1e9 + 7;
const int inf = 1e9;
const long long INF = 1e18;
#ifdef hwe
namespace Jury {
int n, m;
vii edges;
vector<int> color, adj[N];
void test() {
cin >> n >> m;
for (int i = 0; i < n; ++i) adj[i].clear();
color.assign(n, 0);
for (auto &x : color) cin >> x;
edges.assign(m, pii());
for (auto &[x, y] : edges) {
cin >> x >> y;
adj[x].emplace_back(y), adj[y].emplace_back(x);
}
}
int perform_experiment(vector<int> E) {
vector<int> S = color;
for (int i = 0; i < n; ++i)
if (E[i] != -1) S[i] = E[i];
vector<int> vis(n, false);
int num_components = 0;
for (int i = 0; i < n; ++i) if (!vis[i]) {
queue<int> q; q.emplace(i);
vis[i] = true; ++num_components;
while (!q.empty()) {
int u = q.front(); q.pop();
for (auto v : adj[u]) if (!vis[v] && S[v] == S[i]) {
vis[v] = true;
q.emplace(v);
}
}
}
return num_components;
}
}
int perform_experiment(vector<int> E) {
return Jury::perform_experiment(E);
}
#endif
vector<int> adj[N], ke[N];
namespace sub12 {
vector<int> find_colours(int n, vector<int> X, vector<int> Y) {
vector<int> g(n, -1);
for (int i = 0; i < n; ++i) {
for (int c = 0; c < n; ++c) {
vector<int> E(n, c); E[i] = -1;
int foo = perform_experiment(E);
if (foo == 1) {
g[i] = c;
break;
}
}
}
return g;
}
}
void solve(int n, vector<int> A, vector<vector<int>> &components, vector<int> &ans) {
auto count_all = [&](vector<int> E) {
vector<int> vis(n, false);
int num_components = 0;
for (int i = 0; i < n; ++i) if (!vis[i]) {
queue<int> q; q.emplace(i);
vis[i] = true; ++num_components;
while (!q.empty()) {
int u = q.front(); q.pop();
for (auto v : adj[u]) if (E[v] == E[u] && !vis[v]) {
vis[v] = true;
q.emplace(v);
}
}
}
return num_components;
};
for (int color = 0; color < n; ++color) {
int low = 0, high = A.size();
while (true) {
vector<int> E(n, color), local(n, n);
for (int i = low; i < high; ++i)
for (auto &x : components[A[i]]) {
E[x] = -1;
local[x] = A[i];
}
int cnt = count_all(local) - perform_experiment(E);
if (cnt == 0) break;
while (low + 1 < high) {
int mid = (low + high) >> 1;
E.assign(n, color), local.assign(n, n);
for (int i = mid; i < high; ++i)
for (auto &x : components[A[i]]) {
E[x] = -1;
local[x] = A[i];
}
if (perform_experiment(E) < count_all(local)) low = mid;
else high = mid;
}
for (auto &x : components[A[low]])
ans[x] = color;
low = 0, --high;
if (cnt == 1) break;
}
}
}
vector<int> find_colours(int n, vector<int> X, vector<int> Y) {
// if (n <= 50) return sub12::find_colours(n, X, Y);
// identify components
for (int i = 0; i < X.size(); ++i) {
int u = X[i], v = Y[i];
adj[u].emplace_back(v), adj[v].emplace_back(u);
}
auto count = [&](vector<int> E) { // component with color = n
vector<int> vis(n, false);
int num_components = 0;
for (int i = 0; i < n; ++i) if (E[i] == n && !vis[i]) {
queue<int> q; q.emplace(i);
vis[i] = true; ++num_components;
while (!q.empty()) {
int u = q.front(); q.pop();
for (auto v : adj[u]) if (E[v] == E[u] && !vis[v]) {
vis[v] = true;
q.emplace(v);
}
}
}
return num_components;
};
vector<vector<int>> components;
components.emplace_back(vector<int>(1, 0));
for (int u = 1; u < n; ++u) {
vector<int> E(n, n); E[u] = -1;
for (int i = 0; i < components.size(); ++i)
for (auto &x : components[i]) {
E[x] = -1;
}
int if_new = count(E) + components.size() + 1;
int real = if_new - perform_experiment(E);
// cerr << if_new << ' ' << perform_experiment(E) << '\n';
if (real == 0) {
// cerr << u << '\n';
components.emplace_back(vector<int>(1, u));
continue;
}
auto check = [&](int mid) {
vector<int> E(n, n); E[u] = -1;
for (int i = 0; i <= mid; ++i)
for (auto &x : components[i]) {
E[x] = -1;
}
return perform_experiment(E) < count(E) + mid + 2;
};
vector<int> new_component = {u};
for (int _ = 0; _ < real; ++_) {
int low = 0, high = components.size() - 1, compId = -1;
while (low <= high) {
int mid = (low + high) >> 1;
if (check(mid)) high = (compId = mid) - 1;
else low = mid + 1;
}
assert(compId != -1);
for (auto &x : components[compId]) {
new_component.emplace_back(x);
}
swap(components[compId], components.back());
components.pop_back();
}
components.emplace_back(new_component);
}
// Done extract all components
if (components.size() == 1) {
for (int color = 0; color < n; ++color) {
vector<int> E(n, color); E[0] = -1;
if (perform_experiment(E) == 1) return vector<int>(n, color);
}
return vector<int>(n, -1);
}
vector<int> cid(n);
for (int i = 0; i < components.size(); ++i)
for (auto &x : components[i]) cid[x] = i;
for (int i = 0; i < X.size(); ++i) {
int u = cid[X[i]], v = cid[Y[i]];
if (u == v) continue;
ke[u].emplace_back(v), ke[v].emplace_back(u);
}
for (int i = 0; i < n; ++i) remove_duplicate(ke[i]);
vector<int> vis(components.size(), -1);
for (int i = 0; i < components.size(); ++i) if (vis[i] == -1) {
queue<int> q; q.emplace(i);
vis[i] = 0;
while (!q.empty()) {
int u = q.front(); q.pop();
for (auto v : ke[u]) if (vis[v] == -1) {
vis[v] = !vis[u];
q.emplace(v);
}
}
}
vector<int> A, B;
for (int i = 0; i < components.size(); ++i)
if (vis[i] == 0) A.emplace_back(i);
else B.emplace_back(i);
// cerr << "A = ";
// for (auto &x : A) cerr << x << ' ';
// cerr << '\n';
// cerr << "B = ";
// for (auto &x : B) cerr << x << ' ';
// cerr << '\n';
vector<int> ans(n);
solve(n, A, components, ans);
solve(n, B, components, ans);
return ans;
}
#ifdef hwe
signed main() {
ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
#ifdef hwe
freopen("D:/Code/Contests/input.inp", "r", stdin);
// freopen("D:/Code/Contests/output.out", "w", stdout);
#else
#define taskname ""
if (fopen(taskname".inp", "r")) {
freopen(taskname".inp", "r", stdin);
freopen(taskname".out", "w", stdout);
}
#endif
Jury::test();
vector<int> X(Jury::m), Y(Jury::m);
for (int i = 0; i < Jury::m; ++i) tie(X[i], Y[i]) = Jury::edges[i];
vector<int> ans = find_colours(Jury::n, X, Y);
for (auto &x : ans) cerr << x << ' ';
cerr << '\n';
cerr << '\n'; return 0;
}
#endif
