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 D = A.map { it.toDouble() }
    val s = Array<Int> (N + 1) { 0 }
    repeat(N) { s[it + 1] = s[it] + A[it] }
    fun f(c: Int, k: Int): Boolean {
        val i = D.binarySearch(c.toDouble() - 0.1).inv()
        val sum = c * (N - i) + s[i]
        return sum >= c * k
    }
    for (k in 1..N) {
        var l = 0; var r = N / k + 1
        while (l + 1 < r) {
            val c = (l + r) / 2
            fun ok(): Boolean {
                val i = D.binarySearch(c.toDouble() - 0.1).inv()
                val sum = c * (N - i) + s[i]
                return (sum >= c * k)
            }
            if (ok()) l = c else r = c
        }
        println(l)
    }
}
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 }