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 1.8.0) (judge verdict: Runtime Error)

import java.util.Scanner;
import java.io.*;
import java.util.Arrays;

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++) {
			String temp = "";
			if(x.charAt(i) == '0') {
				for(int j = 0; j < x.length(); j++) {
					if(j != i) {
						temp += x.charAt(j);
					}else {
						temp += '1';
					}
				}
				System.out.println(f(temp));
			}else {
				for(int j = 0; j < x.length(); j++) {
					if(j != i) {
						temp += x.charAt(j);
					}else {
						temp += '0';
					}
				}
				System.out.println(f(temp));
			}
			
		}
	}
	
	static int f(String ni) {
		int cnt = 0;
		int kosu = 0;
		while(true) {
			int n = Integer.parseInt(ni, 2);
			kosu = popcount(ni);
			n %= kosu;
			++cnt;
			if(n == 0) {
				break;
			}
			ni = Integer.toBinaryString(n);
		}
		return cnt;
	}
	
	static int popcount(String ni) {
		int cnt = 0;
		for(int i = 0; i < ni.length(); i++) {
			if(ni.charAt(i) == '1') {
				++cnt;
			}
		}
		return cnt;
	}
	
}