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 Go (1.6) (judge verdict: Time Limit Exceeded)

package main
import (
  "fmt"
  "sort"
)
func main() {
  var n,x int
  fmt.Scan(&n)
  a := make([]int,n)
  s := make([]int,n+1)
  for i:=0;i<n;i++ {
    fmt.Scan(&x)
    a[x-1]++
  }
  sort.Ints(a)
  for i:=0;i<n;i++ { s[i+1] = s[i]+a[i] }
  ans := n
  i := n
  for k:=1;k<=n;k++ {
    for {
      for i > 0 && a[i-1] >= ans { i-- }
      if ans*(n-i)+s[i] >= ans*k { break }
      ans--
    }
    fmt.Println(ans)
  }
}