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 = nextInt()
    val a = listOfInt(-1)
    val A = Array<Int>(N) { 0 }
    repeat(N) { A[a[it]] += 1 }
    A.sort()
    val s = Array<Int>(N + 1) { 0 }
    repeat(N) { s[it + 1] = s[it] + A[it] }
    var ans = N; var i = N
    for (k in 1..N) {
        while (true) {
            val ok: () -> Boolean = {
                while (i > 0 && A[i - 1] >= ans) i -= 1
                val sum = ans * (N - i) + s[i]
                sum >= ans * k
            }
            if (ok()) break
            ans -= 1
        }
        println(ans)
    }
}
fun next() = readLine()!!
fun nextInt(delta: Int = 0) = Integer.parseInt(next()) + delta
fun listOfString() = next().split(" ")
fun listOfInt(delta: Int = 0) = listOfString().map { it.toInt() + delta }