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 math
# from collections import defaultdict
import time
def steps(n,p):
  c = 0
  while n:
    c += 1
    n = n%p
    p = bin(n).count('1')
  return c

# n = 200000
# x = "1"*n
n = int(input())
x = input()
incs = 1
decs = 1
p = x.count('1')
ans = []
num = int(x,2)
inc = num%(p+1)
dec = num%(p-1)
start = time.time()
k = -1
for i in range(n-1,-1,-1):
  cp = p
  if x[i] == '0':
    cp += 1
    new = (inc+incs)%cp
  else:
    cp -= 1
    new = (dec-decs)%cp
  k -= 1
  incs = (incs*2)%(p+1)
  decs = (decs*2)%(p-1)
  sol = steps(new,cp)
  if sol==0:
    sol=1
  ans.append(sol)
  # steps(new,cp)
# print(time.time()-start)
ans = ans[::-1]
for x in ans:
  print(x)