Problem:
Score : 400 points

Problem Statement

Let \mathrm{popcount}(n) be the number of 1s in the binary representation of n.
For example, \mathrm{popcount}(3) = 2, \mathrm{popcount}(7) = 3, and \mathrm{popcount}(0) = 0.

Let f(n) be the number of times the following operation will be done when we repeat it until n becomes 0: "replace n with the remainder when n is divided by \mathrm{popcount}(n)." (It can be proved that, under the constraints of this problem, n always becomes 0 after a finite number of operations.)

For example, when n=7, it becomes 0 after two operations, as follows:

\mathrm{popcount}(7)=3, so we divide 7 by 3 and replace it with the remainder, 1.

\mathrm{popcount}(1)=1, so we divide 1 by 1 and replace it with the remainder, 0.

You are given an integer X with N digits in binary.
For each integer i such that 1 \leq i \leq N, let X_i be what X becomes when the i-th bit from the top is inverted.
Find f(X_1), f(X_2), \ldots, f(X_N).

Constraints

1 \leq N \leq 2 \times 10^5

X is an integer with N digits in binary, possibly with leading zeros.

Input

Input is given from Standard Input in the following format:

N
X

Output

Print N lines. The i-th line should contain the value f(X_i).

Sample Input 1

3
011

Sample Output 1

2
1
1

X_1 = 7, which will change as follows: 7 \rightarrow 1 \rightarrow 0. Thus, f(7) = 2.

X_2 = 1, which will change as follows: 1 \rightarrow 0. Thus, f(1) = 1.

X_3 = 2, which will change as follows: 2 \rightarrow 0. Thus, f(2) = 1.

Sample Input 2

23
00110111001011011001110

Sample Output 2

2
1
2
2
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
3

Solution in JavaScript (Node.js 12.16.1) (judge verdict: Time Limit Exceeded)

function main(input) {
  const n = parseInt(input[0]);
  const x = {};
  x.two = input[1];
  x.ten = parseInt(x.two, 2);

  const popcount = x.two.split("").reduce((acc, value) => {
    return ((value==1)?(acc+1):(acc));
  }, 0);

  for(let i=0;i<n;i++){
    const k = JSON.parse(JSON.stringify(x));
    let new_k = k.two.split("");
    if(new_k[i]==="0"){
      new_k[i]=1;
    }else{
      new_k[i]=0;
    }
    k.two = new_k.join("");
    k.ten = parseInt(k.two, 2);

    let cnt = 0;

    while(k.ten !== 0){
      const popcount = k.two.split("").reduce((acc, value) => {
        return ((value==1)?(acc+1):(acc));
      }, 0);
      k.ten = k.ten % popcount;
      k.two = k.ten.toString(2);
      cnt++;
    }
    console.log(cnt);
  }
}
main(require('fs').readFileSync('/dev/stdin', 'utf8').trim().split("\n"));