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 Java (OpenJDK 11.0.6) (judge verdict: Runtime Error)

import java.util.Scanner;
import java.util.List;
import java.util.ArrayList;

public class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    String X = sc.next();
    for(int i=0; i<X.length(); i++){
      int count=0;
      String target = chX(X,i);
      int targ = bit2num(target);
      while(targ != 0){
        int pcount=popcount(target);
        if (pcount == 0){
          break;
        }
        targ = targ%pcount;
        target=Integer.toBinaryString(targ);
        count++;
      }
      System.out.println(count);
    }
  }
  
  public static String chX(String X,int index){
    String newstr ="";
    if (X.charAt(index) == '1'){
      newstr=X.substring(0,index)+"0"+X.substring(index+1);
    } else {
      newstr=X.substring(0,index)+"1"+X.substring(index+1);
    }
    return newstr;
  }

  public static int bit2num(String x){
    return Integer.parseInt(x,2);
  }
  
  public static int popcount(String target){
    int count = 0;
    for (char x : target.toCharArray()){
      if(x == '1'){
        count++;
      }
    }
    return count;
  } 
}