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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import sys
input = sys.stdin.readline

def main():
  n = int(input())
  x = input()
  count = 0
  sub = 1
  last = [None]*n
  for i in range(n):
    if x[i] == "1":
      count += 1
            
  if count == 0:
    for i in range(n):
      print(1)
    sys.exit()
  if count == 1:
    if x[-1] == "1":
      for i in range(n-1):
        print(2)
      print(0)
      sys.exit()
    else:
      for i in range(n-1):
        if x[i] == "1":
          print(0)
        else:
          print(1)
      print(2)
      sys.exit()

  sub1, sub2 = 1, 1
  num1, num2 = 0, 0
  for i in range(n):
    if count-1 == 0:
      sub1 = 0
    last[i] = [sub1, sub2]
    if x[n-i-1] == "1":
      num1 += sub1
      num2 += sub2
      num1 %= count-1
      num2 %= count+1
    sub1 *= 2
    sub2 *= 2
    sub1 %= count-1
    sub2 %= count+1
            
    
    
  key = [0]*(2**18+1)
  for i in range(1, 2**18):
    c = 0
    for j in range(18):
      if (i>>j)&1:
        c += 1
    judge = i%c
    key[i] = key[judge] + 1

  for i in range(n):
    if x[i] == "1":
      judge = (num1+count-1-last[n-1-i][0])%(count-1)
      print(1+key[judge])
    else:
      judge = (num2+last[n-1-i][1])%(count+1)
      print(1+key[judge])

if __name__ == "__main__":
  main()