Problem:
Score : 600 points

Problem Statement

Takahashi has N cards. The i-th of these cards has an integer A_i written on it.

Takahashi will choose an integer K, and then repeat the following operation some number of times:

Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.)

For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation.

Constraints

1 \le N \le 3 \times 10^5

1 \le A_i \le N

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \ldots A_N

Output

Print N integers.
The t-th (1 \le t \le N) of them should be the answer for the case K=t.

Sample Input 1

3
2 1 2

Sample Output 1

3
1
0

For K = 1, we can do the operation as follows:

Choose the first card to eat.

Choose the second card to eat.

Choose the third card to eat.

For K = 2, we can do the operation as follows:

Choose the first and second cards to eat.

For K = 3, we cannot do the operation at all. Note that we cannot choose the first and third cards at the same time.

Sample Input 2

5
1 2 3 4 5

Sample Output 2

5
2
1
1
1

Sample Input 3

4
1 3 3 3

Sample Output 3

4
1
0
0

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] sa = br.readLine().split(" ");
		int n = Integer.parseInt(sa[0]);
		sa = br.readLine().split(" ");
		Map<Integer, Integer> map = new HashMap<>();
		for (int i = 0; i < n; i++) {
			addCntMap(map, Integer.parseInt(sa[i]));
		}
		br.close();

		List<Integer> list = new ArrayList<>(map.size());
		for (Integer o : map.values()) {
			list.add(o);
		}
		Collections.sort(list);

		Integer[] sum = list.toArray(new Integer[0]);
		int len = sum.length;
		for (int i = 1; i < len; i++) {
			sum[i] += sum[i - 1];
		}
		PrintWriter pw = new PrintWriter(System.out);
		int ans = n;
		int x = len - 1;
		for (int i = 1; i <= n; i++) {
			for ( ; ans >= 0; ans--) {
				for ( ; x > 0; x--) {
					if (list.get(x) <= ans) {
						break;
					}
				}
				int val = sum[x];
				val += (len - 1 - x) * ans;
				if (val >= i * ans) {
					pw.println(ans);
					break;
				}
			}
		}
		pw.flush();
	}

	static void addCntMap(Map<Integer, Integer> map, Integer key) {
		if (map.containsKey(key)) {
			map.put(key, map.get(key) + 1);
		} else {
			map.put(key, 1);
		}
	}
}