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 JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

function Main(input) {
  input=input.split("\n");
  if(input[input.length-1]===''){
    input.pop();
  }
  const N=input[0].split(' ')[0]-0;
  const A=input[1].split(' ').map(e=>{
    return e-0;
  }).sort((a,b)=>{
    return a-b;
  });
  var array=[];
  var temp=0;
  var previous=0;
  A.forEach(e=>{
    if(e!==previous){
      array.push(temp);
      previous=e;
      temp=1;
    }else{
      temp++;
    }
  });
  array.push(temp);
  array.shift();
  array.sort((a,b)=>{
    return a-b;
  });
  //console.log(array);
  var upperbound;
  for(var i=1;i<=N;i++){
    upperbound=0;
    for(var j=0;j<array.length-i+1;j++){
      upperbound+=array[j];
    }
    console.log(Math.min(Math.floor(N/i),upperbound*i));
  }
}




//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));