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: Time Limit Exceeded)

import copy
POPCOUNT_TABLE16 = [0] * (2*10**5+1)
for index in range(len(POPCOUNT_TABLE16)):
    POPCOUNT_TABLE16[index] = (index & 1) + POPCOUNT_TABLE16[index >> 1]

def popcnt(v):
    return (POPCOUNT_TABLE16[ v        & 0xffff] +
            POPCOUNT_TABLE16[(v >> 16) & 0xffff] +
            POPCOUNT_TABLE16[(v >> 32) & 0xffff] +
            POPCOUNT_TABLE16[(v >> 48)         ])
N = int(input())
X = list(input())
X_int = 0
Xf = [[0 for i in range(2)] for i in range(2*(10**5))]

SUM = 0
for i in range(N):
    if X[i] == '1':
        SUM += 1
    

for i in range(N):
    if X[i] == '1':
        X[i] = '0'
        Xf[i][1] = SUM - 1
        X_c = copy.copy(X)
        Xf[i][0] = int(''.join(X_c), 2)
        X[i] = '1'
    elif X[i] == '0':
        X[i] = '1'
        Xf[i][1] = SUM + 1
        X_c = copy.copy(X)
        Xf[i][0] = int(''.join(X_c), 2)
        X[i] = '0'
    
for i in range(N):
    ans = 0
    flg = 0
    while Xf[i][0] > 0:
        ans += 1
        if flg == 0:
            Xf[i][0] = Xf[i][0] % Xf[i][1]
            flg =1
        else:
             Xf[i][0]= Xf[i][0]%popcnt(Xf[i][0])
    print(ans)