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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

import java.util.Scanner

fun main(args: Array<String>) {
	val scn = Scanner(System.`in`)
	val n = scn.nextInt()
	val cnts = mutableMapOf<Int, Int>()
	repeat(n){
		val a = scn.nextInt()
		cnts[a] = cnts.getOrElse(a){0} + 1
	}
	val keys = cnts.keys.sortedBy { cnts[it] }
	for (i in 1..n){
		if (cnts.size<i) {
			println(0)
			continue
		}
		val Cs = keys.map { cnts[it]!! }.toMutableList()
		var ans = 0
		Cs.forEachIndexed { l, c ->
			if (l<=Cs.size-i) {
				ans += c
				for (p in l + 1 until l + i) Cs[p] -= c
			}
		}
		println(ans)
	}
}