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: Time Limit Exceeded)

fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val cs = readLine()!!.split(" ").take(n).map { it.toInt() }.toList()


    val counts = cs.groupBy { it }.mapValues { it.value.count() }.values.sorted()

    println(n)
    for (k in (2..n)) {
        calc(k, counts)
    }
}

fun calc(k: Int, list: List<Int>) {
    var mList = list.toMutableList();
    var count = 0;
    while (true) {      
        if (mList.size < k) {
            println(count)
            break
        }
        val last = mList.size
        ((last - k) until last).forEach {
            mList[(it)] = mList[it]-1
        }
        mList = mList.filter { it != 0 }.sorted().toMutableList()
        count++
    }
}