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 #追加
sys.setrecursionlimit(500*500) #追加

# x^n % mod
def pow_k(x, n, mod):
  if n == 0:
    return 1

  K = 1
  while n > 1:
    if n % 2 != 0:
      K = (x * K) % mod
        
    x = (x * x) % mod

    n //= 2

  return (x * K) % mod

def func(dic, n):
  
  if n in dic:
    return dic[n]
  
  if n == 0:
    return 0
  
  t = bin(n)
  tmp = len(t) - len(t.replace('1','' ))

  n2 = n % tmp
    
  dic[n] = 1 + func(dic, n2)
  
  return dic[n]


n = int(input())
x = input()

num1 = len(x.replace('0', ''))

x_rev = list(reversed(x))

array_minus = [-1] * n
array_plus = [-1] * n

minus = 0
plus = 0
for i in range(n):
  if x_rev[i] == '0':
    array_minus[i] = 0
    array_plus[i] = 0
  
  else:
    array_minus[i] = pow_k(2, i, num1-1)
    minus += array_minus[i]
    minus %= num1-1
    array_plus[i] = pow_k(2, i, num1+1)
    plus += array_plus[i]
    plus %= num1+1
    
dic = {}
for i in range(n):
  if x[i] == '0':
    tmp = pow_k(2, n-1-i, num1+1) + plus
    tmp %= num1+1
  
  else:
    tmp = minus - array_minus[n-i-1]
    tmp %= num1 -1
    
  print(func(dic, tmp)+1)