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)

def solve():
  def popcount(x):
    S = format(x,'b')
    cnt = 0
    for s in S:
      if s=='1':
        cnt+=1
    return cnt
  N = int(input())
  X = input()
  num = 0
  pcnt = 0
  for i, x in enumerate(X):
    if x=='1':
      pcnt += 1
      num += 2**(N-i-1)
  a = num//pcnt
  b = num%pcnt
  for i, x in enumerate(X):
    ans = 1
    if x=='1':
      n1 = (a+b-2**(N-i-1))%(pcnt-1)
    else:
      n1 = (b-a+2**(N-i-1))%(pcnt+1)
    while n1 >5:
      pc = popcount(n1)
      n1 = n1%pc
      ans +=1
    if n1==0:
      print(ans)
    elif n1==1:
      print(ans+1)
    elif n1==2:
      print(ans+1)
    elif n1==3:
      print(ans+2)
    elif n1==4:
      print(ans+1)
    elif n1==5:
      print(ans+2)
solve()