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.*;
import java.lang.*;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n;
        String s;
        int[] dp = new int[200001];
        n = Integer.valueOf(in.nextLine());
        s = in.nextLine();

        dp[0] = 0;
        for(int i=1; i<= 200000; i++){
            dp[i] = dp[i%Integer.bitCount(i)]+1;
        }

        int bits = 0;
        for(int i=0; i<n; i++){
            if(s.charAt(i)=='1') bits++;
        }

        // calculate X % ( popcount(X) +/- 1 ) 
        int x1 = 0;
        int x2 = 0;
        long b1 = 1;
        long b2 = 1;
        for(int i=n-1; i>=0; i--){
            if(s.charAt(i)=='1'){
                if(bits-1>0) x1 += b1 % (bits-1);
                x2 += b2 % (bits+1);
            }
            if(bits-1>0) b1 = (b1*2)%(bits-1);
            b2 = (b2*2)%(bits+1);
        }

        for(int i=0; i<n; i++){
            int xi = 0;
            int xbits = 0;
            if(s.charAt(i)=='1'){
                xbits = bits-1;
                if(xbits>0){
                    xi = x1 - (int) Math.round(Math.pow(2, n-i-1)) % (xbits);
                    xi = xi % xbits;
                }else{
                    print(0);
                    continue;
                }
            }else{
                xbits = bits+1;
                xi = x2 + (int) Math.round(Math.pow(2, n-i-1)) % (xbits);
                xi = xi % xbits;
            }
            print(dp[xi]+1);
        }

        in.close();
    }

    private static void print(Object obj){
        System.out.println(obj);
    }
} // javac Main.java; java Main < in > out