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;

public class Main {

  public static void main(String[] args) {
    Scanner scan = new Scanner(System.in);
    String str = scan.nextLine();
    int n = Integer.parseInt(str);
    str = scan.nextLine();
    boolean[] bool = new boolean[n];
    for (int i = 0; i < n; i++) {
      bool[i] = str.charAt(i) == '1';
    }
    for (int i = 0; i < n; i++) {
      // Xiを求める
      StringBuffer sb = new StringBuffer();
      for (int j = 0; j < n; j++) {
        sb.append(bool[j]^i==j? '1' : '0');
      }
//      System.out.println(sb.toString());
      int current = Integer.parseInt(sb.toString(), 2);
      int count = 0;
      while (current != 0){
        count++;
        final int popcount = popcount(current);
        if (popcount == 0) break;
        current %= popcount;
      }
      System.out.println(count);
    }
  }
  private static int popcount(int number){
    final String bin = Integer.toBinaryString(number);
    int count = 0;
    for (int i = 0; i < bin.length(); i++) {
      if (bin.charAt(i) == '1') {
        count++;
      }
    }
    return count;
  }
}