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: Accepted)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);

    int N = scanner.nextInt();
    int[] freq = new int[N];
    for (int i = 0; i < N; i++) {
      int a = scanner.nextInt() - 1;
      freq[a]++;
    }
    Arrays.sort(freq);
    long[] cumsum = new long[N];
    cumsum[0] = freq[0];
    for (int i = 1; i < N; i++) {
      cumsum[i] = cumsum[i - 1] + freq[i];
    }

    long[] res = new long[N];
    for (int i = 0; i < N; i++) res[N - i - 1] = upperBound(freq, cumsum, i, N);

    StringBuilder sb = new StringBuilder();
    for (int i = 0; i < N; i++) sb.append(res[i]).append('\n');
    System.out.print(sb.toString());
  }

  public static long upperBound(int[] freq, long[] cumsum, int offset, int N) {
    long left = freq[offset];
    long right = cumsum[N - 1] + 1;
    while (right - left > 1) {
      long mid = (left + right) / 2;
      int idx = upperBound(freq, mid);
      if (cumsum[idx] >= (idx - offset + 1) * mid) {
        left = mid;
      } else {
        right = mid;
      }
    }
    return left;
  }

  public static int upperBound(int[] a, long k) {
    int left = -1;
    int right = a.length;
    while (right - left > 1) {
      int mid = (left + right) / 2;
      if (a[mid] < k) {
        left = mid;
      } else {
        right = mid;
      }
    }
    return left;
  }
}