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: Runtime Error)

# -*- coding: utf-8 -*-
N = int(input())
X = input()
X_10 = 0
popcount_X = 0

def popcount(n):
  return bin(n).count("1")

def f_func(n):
  popcnt = popcount(n)
  if popcnt == 0:
    return 0
  return n % popcnt

for i in range(N):
  j = N - (i + 1)
  X_10 += int(X[i]) * 2 ** j
  if X[i] == '1':
    popcount_X += 1

popcount_X_plus = popcount_X + 1
popcount_X_minus = popcount_X - 1
if popcount_X_plus == 0:
  fX_plus = 0
else:
  fX_plus = X_10 % popcount_X_plus

fX_minus = X_10 % popcount_X_minus


for i in range(N):
  j = N - (i + 1)
  
  Xi = 0
  f = 0
  ans = 1
  
  if X[i] == '0':
    Xi = X_10 + 2**j
    f = (fX_plus + 2**j % popcount_X_plus) % popcount_X_plus
    
  elif X[i] == '1':
    Xi = X_10 - 2**j
    if popcount_X_minus == 0:
      f = 0
    else:
      f = (fX_minus - 2**j % popcount_X_minus) % popcount_X_minus
      
  
  while f > 0:
    f = f_func(f)
    ans += 1
  print(ans)