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)

import sys
sys.setrecursionlimit(10**6)
from functools import lru_cache

def input():
    return sys.stdin.readline().rstrip()

@lru_cache(maxsize =None)
def tc(n):
    if n ==0:
        return 0

    y =n
    count =0
    while y:
     if y%2==1:
         count +=1
     y=y//2
    ans =n % count
    if ans ==0:
     return 1
    else:
     return tc(ans) +1



def main():
    N = int(input())
    x = input()
    X = int(x,2)

    const = 0
    for i in range(N):
        if x[i] =="1":
            const +=1
    if const ==0:
        for i in range(N):
            print(1)
        exit()
    if const ==1:
        if x[-1] =="0":
            for i in range(N-1):
                if x[i] =="1":
                    print(0)
                else:
                    print(1)
            print(2)
        else:
            for i in range(n-1):
                print(2)
            print(0)
        exit()

    xm = X % (const - 1)
    xp = X % (const +1)

    for i in range(N-1, -1, -1):
        if x[N-i-1] =="0":
            t = xp + pow(2,i,const +1)
            t %= const +1
        else:
            t = xm - pow(2,i,const -1)
            t %= const -1






        print(tc(t)+1)









if __name__ == "__main__":
    main()