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 Python (3.8.2) (judge verdict: Runtime Error)

# -*- coding: utf-8 -*-

import sys
import math

def saiki(n,saiki_one_count,do_count):
    do_count += 1
    mod = n % saiki_one_count
    if mod == 0:
        return do_count
    saiki_one_count = bin(mod).count("1")
    return saiki(mod,saiki_one_count,do_count)
def main():
    input = sys.stdin.readline
    N = int(input())
    x = input()
    x_list = list(x)[:-1]
    x_list = [int(value) for value in x_list]
    one_count = x_list.count(1)
    sum_x = 0
    for i in range(len(x_list)):
        if x_list[N -1 - i] == 1:
            sum_x += 2 ** i

    for i in range(len(x_list)):
        current_sum_x = 0
        current_one_count = 0
        if x_list[i] == 0:
            current_one_count = one_count + 1
            current_sum_x = sum_x + 2 ** (N - 1 - i)
        else:
            current_one_count = one_count - 1
            current_sum_x = sum_x - 2 ** (N - 1 - i)
        do_count = saiki(current_sum_x,current_one_count,0)
        print(do_count)
    return


if __name__ == '__main__':
    main()