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)

import sys, bisect, math, itertools, heapq, collections
from operator import itemgetter
# a.sort(key=itemgetter(i)) # i番目要素でsort
from functools import lru_cache
# @lru_cache(maxsize=None)
sys.setrecursionlimit(10**8)
input = sys.stdin.readline
INF = float('inf')
mod = 10**9 + 7
eps = 10**-7


def inp():
    '''
    一つの整数
    '''
    return int(input())


def inpl():
    '''
    一行に複数の整数
    '''
    return list(map(int, input().split()))


def str_inp():
    '''
    文字列をリストとして読み込む
    '''
    return list(input()[:-1])


@lru_cache(maxsize=None)
def countbits(n):
    res = 0
    while n:
        res += n % 2
        n //= 2
    return res


n = inp()
x = str_inp()
dp = collections.defaultdict(lambda: -1)
dp[0] = 0
bits_amount = 0
ans = []
for i in range(n):
    bits_amount += int(x[i])
minus_val = 0
plus_val = 0
if bits_amount != 0:
    for i in range(n):
        if int(x[i]):
            minus_val += pow(2, n - i - 1, bits_amount - 1)
            minus_val %= (bits_amount - 1)
if bits_amount != n:
    for i in range(n):
        if int(x[i]):
            plus_val += pow(2, n - i - 1, bits_amount + 1) % (bits_amount + 1)
            plus_val %= (bits_amount + 1)
for i in range(n):
    if int(x[i]):  # 1->0
        now_val = (minus_val - pow(2, n - i - 1, bits_amount - 1)) % (bits_amount - 1)
    else:
        now_val = (plus_val + pow(2, n - i - 1, bits_amount + 1)) % (bits_amount + 1)
    path = [now_val]
    while True:
        if dp[now_val] != -1:
            break
        now_val = now_val % countbits(now_val)
        path.append(now_val)
    tmp = dp[now_val]
    for j in range(1, len(path)):
        tmp += 1
        dp[path[len(path) - j - 1]] = tmp
    ans.append(dp[path[0]])
for i in ans:
    print(i + 1)