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



Sample input:
3
011


Sample output:
2
1
1

Submission status: Time Limit Exceeded

Solution code:
def main():
    N = int(input())
    X = input()
    lowNumber = [1, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 4, 2, 3, 2, 3, 2, 2, 3, 4, 2, 3, 3, 4, 3, 3, 3, 3, 2, 3, 2, 3, 2, 3, 3, 4, 2, 3, 2, 4, 3, 3, 3, 3, 2, 3, 3, 4, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 4, 2, 3, 2, 3, 2, 2, 3, 4, 2, 3, 3, 4, 3, 3, 3, 3, 2, 2, 3, 4, 2, 3, 3, 3, 3, 3, 3, 3, 2, 4, 3, 4, 2, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 2, 3, 2, 4, 3, 3, 3, 2, 2, 3, 4, 4, 2, 3, 3, 4, 3, 4, 2, 3, 2, 3, 2, 3, 2, 3, 3, 4, 2, 3, 2, 4, 3, 3, 3, 4, 2, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 4, 4, 2, 3, 2, 4, 3, 3, 3, 3, 2, 3, 3, 3, 2, 4, 3, 3, 3, 3, 3, 3, 2, 3, 3, 4, 2, 2, 3, 3, 4, 4, 3, 3, 2, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 2, 2, 3, 4, 3, 3, 3, 3, 2, 4, 3, 4, 2, 3, 4, 4, 2, 4, 2, 3, 3, 3, 3, 3, 2, 3, 2, 4, 2, 4, 3, 3, 3, 4, 3, 3, 2, 3, 3, 4, 3, 4, 2, 3, 4, 4, 3, 3, 2, 3, 3, 4, 2, 3, 2, 3, 2, 2, 3, 4, 2, 3, 3, 4, 3, 3, 3, 3, 2, 2, 3, 4, 2, 3, 3, 3, 3, 3, 3, 4, 2, 2, 3, 4, 2, 3, 3, 4, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 4, 3, 3, 3, 3, 2, 3, 2, 4, 2, 4, 3, 4, 3, 4, 2, 3, 2, 2, 3, 4, 2, 3, 3, 3, 3, 3, 3, 3, 2, 4, 3, 4, 2, 3, 3, 3, 2, 3, 3, 3, 2, 2, 3, 4, 4, 3, 3, 3, 3, 3, 3, 2, 2, 3, 4, 4, 2, 3, 3, 4, 3, 4, 2, 4, 2, 3, 2, 4, 3, 3, 3, 3, 3, 4, 2, 3, 3, 4, 3, 4, 2, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 4, 4, 3, 3, 3, 4, 2, 2, 3, 4, 2, 3, 2, 4, 3, 4, 2, 3, 3, 3, 3, 3, 2, 3, 3, 4, 2, 2, 3, 3, 4, 4, 3, 3, 2, 4, 3, 4, 3, 4, 2, 4, 2, 4, 3, 3, 2, 3, 4, 4, 3, 3, 3, 3, 2, 4, 3, 4, 2, 3, 4, 4, 2, 4, 2, 3, 2, 2, 3, 4, 4, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 4, 2, 3, 3, 4, 3, 4, 2, 3, 4, 4, 3, 3, 2, 4, 3, 4, 3, 4, 2, 3, 3, 3, 4, 4, 2, 3, 3, 4, 3, 4, 3, 4, 2, 3, 2, 3, 2, 3, 3, 4, 2, 3, 2, 4, 3, 3, 3, 3, 2, 3, 3, 4, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 4, 2, 3, 2, 4, 3, 3, 3, 3, 2, 3, 3, 2, 2, 3, 4, 3, 3, 3, 3, 4, 2, 2, 3, 4, 2, 3, 2, 3, 3, 4, 3, 3, 2, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 2, 3, 2, 4, 3, 3, 3, 2, 2, 3, 4, 4, 2, 3, 3, 4, 3, 4, 2, 4, 3, 3, 3, 3, 2, 4, 3, 4, 2, 3, 4, 3, 2, 4, 3, 2, 2, 2, 3, 4, 4, 4, 2, 3, 3, 4, 3, 4, 2, 2, 3, 4, 2, 3, 2, 4, 3, 3, 3, 3, 2, 3, 3, 3, 2, 4, 3, 3, 3, 3, 3, 3, 2, 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2, 4, 3, 3, 3, 4, 3, 4, 4, 4, 3, 4, 2, 2, 3, 4, 3, 4, 3, 3, 3, 3, 4, 4, 3, 3, 3, 4, 3, 4, 3, 4, 2, 3, 3, 4, 3, 4, 3, 3, 3, 4, 2, 3, 3, 3, 2, 4, 4, 4, 3, 4, 2, 4, 3, 4, 3, 2, 3, 4, 4, 4, 3, 4, 4, 4, 3, 3, 3, 3, 3, 4, 2, 4, 3, 4, 3, 4, 3, 3, 3, 3, 4, 4, 4, 4, 3, 4, 4, 4, 3, 2, 2, 3, 4, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 4, 4, 2, 3, 2, 3, 3, 4, 3, 3, 3, 3, 3, 2, 3, 3, 4, 4, 2, 3, 4, 4, 2, 4, 2, 4, 2, 4, 3, 4, 3, 4, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 4, 3, 4, 2, 3, 4, 4, 4, 3, 3, 3, 2, 3, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 3, 2, 3, 4, 2, 3, 2, 4, 3, 4, 3, 3, 3, 4, 2, 4, 3, 4, 3, 4, 4, 4, 3, 2, 2, 3, 4, 4, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 4, 2, 4, 3, 4, 3, 4, 3, 3, 2, 3, 4, 3, 4, 4, 3, 4, 2, 4, 3, 4, 2, 4, 3, 4, 2, 2, 3, 4, 4, 4, 2, 3, 4, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 2, 3, 4, 3, 3, 4, 4, 4, 3, 3, 3, 2, 4, 3, 4, 3, 3, 3, 4, 4, 4, 3, 2, 3, 3, 4, 4, 3, 4, 3, 3, 3, 3, 2, 4, 2, 4, 3, 4, 3, 4, 3, 4, 2, 4, 2, 3, 3, 3, 4, 4, 3, 3, 4, 4, 2, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 2, 4, 3, 3, 3, 4, 3, 3, 2, 3, 4, 4, 4, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 2, 3, 4, 4, 4, 4, 3, 3, 2, 3, 3, 3, 3, 3, 2, 4, 3, 4, 2, 4, 3, 4, 3, 4, 3, 2, 3, 4, 4, 4, 3, 3, 2, 4, 3, 4, 3, 4, 2, 4, 4, 4, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 2, 4, 3, 4, 3, 4, 3, 4, 3, 4, 2, 2, 3, 4, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 2, 4, 3, 4, 2, 3, 2, 3, 3, 4, 3, 3, 3, 4, 3, 4, 2, 4, 3, 4, 4, 4, 3, 3, 3, 3, 4, 4, 3, 3, 4, 4, 2, 4, 3, 3, 4, 3, 3, 4, 3, 4, 3, 4, 3, 3, 4, 4, 4, 3, 3, 4, 3, 3, 2, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 4, 3, 3, 3, 3, 4, 4, 2, 3, 3, 4, 3, 4, 3, 2, 3, 4, 3, 4, 3, 4, 3, 3, 4, 4, 3, 3, 2, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 2, 3, 2, 4, 3, 4, 3, 4, 3, 4, 3, 4, 2, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 2, 3, 2, 4, 3, 3, 3, 2, 2, 3, 4, 4, 2, 3, 3, 4, 3, 4, 2, 3, 3, 3, 3, 3, 2, 4, 3, 4, 2, 3, 4, 3, 2, 4, 3, 3, 2, 2, 3, 4, 4, 4, 2, 2, 3, 4, 3, 3, 2, 3, 2, 4, 3, 3, 3, 4, 2, 2, 3, 4, 2, 3, 2, 4, 3, 4, 2, 4, 2, 3, 4, 4, 2, 3, 3, 3, 3, 4, 2, 3, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 3, 2, 4, 3, 4, 2, 4, 3, 4, 4, 4, 2, 3, 3, 3, 2, 4, 2, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 2, 3, 2, 4, 2, 4, 3, 3, 3, 4, 3, 3, 2, 3, 3, 4, 3, 4, 2, 4, 4, 4, 3, 3, 2, 3, 4, 4, 2, 3, 4, 3, 2, 4, 3, 2, 3, 3, 3, 3, 3, 3, 2, 4, 3, 4, 3, 4, 2, 2, 3, 4, 3, 3, 4, 4, 2, 4, 3, 3, 2, 3, 2, 4, 3, 4, 2, 3, 3, 4, 3, 3, 2, 4, 3, 4, 3, 4, 2, 3, 3, 3, 4, 4, 2, 3, 3, 4, 3, 4, 3, 4, 2, 4, 3, 3, 2, 3, 2, 4, 3, 4, 3, 4, 3, 4, 3, 4, 2, 3, 4, 4, 2, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 4, 4, 2, 3, 3, 4, 3, 4, 2, 3, 2, 3, 2, 4, 3, 3, 3, 2, 3, 4, 2, 3, 3, 3, 2, 4, 2, 2, 3, 4, 4, 4, 2, 3, 3, 4, 3, 3, 2, 3, 3, 4, 2, 4, 2, 2, 3, 3, 4, 4, 2, 3, 2, 4, 3, 4, 3, 3, 2, 3, 4, 4, 2, 3, 3, 3, 3, 4, 2, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 2, 4, 3, 4, 3, 4, 3, 4, 3, 2, 4, 4, 2, 3, 3, 3, 3, 4, 2, 4, 3, 4, 3, 4, 3, 4, 3, 3, 2, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 2, 3, 3, 4, 3, 4, 2, 2, 4, 4, 3, 3, 2, 3, 2, 4, 3, 4, 2, 4, 3, 2, 3, 4, 2, 3, 4, 4, 2, 4, 3, 3, 3, 4, 3, 2, 2, 3, 4, 4, 3, 3, 2, 4, 3, 4, 3, 3, 2, 2, 3, 4, 4, 4, 3, 4, 2, 3, 3, 3, 3, 3, 4, 4, 3, 4, 2, 3, 3, 3, 2, 4, 2, 4, 3, 4, 3, 4, 3, 3, 3, 3, 4, 4, 2, 4, 3, 4, 3, 3, 3, 4, 3, 2, 3, 4, 2, 3, 2, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 2, 3, 3, 3, 3, 3, 4, 4, 2, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 2, 4, 3, 4, 2, 3, 4, 3, 2, 4, 3, 4, 2, 2, 3, 4, 4, 4, 2, 3, 3, 4, 3, 3, 2, 4, 3, 4, 2, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 3, 2, 3, 2, 4, 3, 4, 3, 4, 3, 4, 3, 3, 2, 4, 3, 4, 3, 4, 2, 4, 2, 4, 3, 2, 2, 3, 4, 4, 4, 4, 2, 3, 3, 4, 3, 4, 2, 2, 3, 4, 4, 4, 3, 3, 3, 4, 3, 4, 2, 4, 3, 4, 3, 3, 4, 4, 4, 4, 3, 3, 2, 4, 3, 4, 3, 4, 3, 3, 4, 3, 3, 4, 3, 4, 3, 4, 2, 3, 4, 3, 2, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 3, 2, 3, 4, 4, 3, 3, 3, 4, 3, 4, 3, 4, 4, 3, 3, 3, 3, 3, 2, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 3, 4, 4, 2, 4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 4, 2, 4, 3, 3, 2, 4, 3, 4, 3, 2, 3, 4, 4, 4, 3, 3, 2, 3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 4, 3, 4, 3, 4, 4, 3, 3, 2, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 2, 4, 3, 4, 3, 3, 3, 4, 2, 2, 3, 4, 4, 4, 2, 3, 3, 4, 3, 4, 2, 4, 3, 4, 2, 4, 2, 3, 3, 3, 2, 4, 2, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 3, 2, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 2, 3, 2, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 2, 4, 3, 4, 3, 4, 2, 3, 4, 4, 4, 4, 3, 3, 3, 4, 3, 4, 3, 4, 3, 2, 4, 3, 3, 3, 3, 3, 4, 4, 2, 4, 3, 4, 3, 4, 3, 4, 4, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 4, 3, 4, 3, 3, 2, 3, 2, 4, 3, 4, 3, 4, 3, 4, 3, 3, 2, 3, 4, 4, 2, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 3, 2, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 2, 3, 3, 3, 3, 3, 4, 4, 2, 3, 2, 3, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 2, 3, 4, 2, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 2, 3, 4, 4, 4, 3, 3, 4, 2, 3, 3, 4, 3, 4, 2, 3, 3, 4, 3, 3, 3, 3, 2, 4, 3, 3, 3, 4, 2, 2, 3, 4, 2, 3, 2, 4, 3, 4, 2, 3, 2, 3, 4, 4, 2, 3, 3, 4, 3, 4, 2, 3, 3, 3, 4, 4, 2, 4, 3, 4, 3, 4, 2, 2, 2, 4, 3, 3, 2, 3, 2, 4, 4, 4, 2, 4, 3, 2, 3, 4, 2, 3, 4, 4, 2, 4, 3, 4, 2, 2, 3, 4, 4, 3, 3, 3, 3, 4, 2, 3, 3, 4, 3, 4, 2, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 2, 3, 3, 3, 2, 4, 2, 4, 3, 4, 3, 4, 3, 3, 3, 3, 4, 4, 2, 4, 3, 2, 3, 3, 3, 3, 3, 3, 4, 4, 2, 3, 2, 4, 3, 4, 2, 4, 3, 4, 3, 3, 2, 3, 4, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 3, 4, 4, 4, 4, 3, 3, 2, 4, 3, 4, 2, 2, 3, 4, 3, 3, 4, 4, 2, 4, 3, 3, 2, 4, 3, 4, 3, 4, 3, 3, 4, 3, 3, 4, 3, 4, 3, 3, 3, 4, 2, 3, 3, 3, 4, 4, 2, 3, 3, 4, 3, 4, 3, 4, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 2, 3, 4, 4, 2, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 4, 3, 2, 3, 4, 2, 3, 4, 3, 4, 4, 3, 3, 2, 3, 4, 4, 2, 3, 3, 2, 3, 4, 2, 3, 3, 3, 2, 4, 3, 3, 3, 4, 3, 2, 3, 4, 3, 3, 4, 4, 2, 4, 3, 3, 4, 4, 2, 2, 3, 3, 4, 4, 2, 3, 2, 4, 3, 4, 3, 3, 3, 2, 3, 4, 4, 4, 3, 4, 2, 3, 3, 4, 3, 2, 3, 4, 2, 3, 3, 3, 3, 3, 2, 4, 3, 4, 3, 4, 3, 4, 3, 2, 3, 3, 4, 4, 2, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 2, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 2, 3, 3, 2, 3, 3, 4, 4, 2, 3, 4, 4, 2, 3, 3, 2, 3, 4, 2, 4, 3, 2, 3, 4, 2, 3, 4, 4, 2, 4, 3, 3, 3, 4, 3, 4, 3, 4, 3, 2, 4, 3, 3, 3, 3, 3, 4, 4, 2, 2, 3, 4, 4, 4, 3, 4, 2, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 3, 4, 3, 3, 4, 4, 2, 4, 3, 4, 3, 3, 3, 4, 3, 2, 3, 4, 4, 3, 3, 3, 3, 3, 2, 3, 2, 4, 3, 4, 3, 4, 3, 3, 2, 3, 3, 3, 3, 3, 4, 4, 2, 3, 3, 3, 3, 4, 3, 3, 2, 2, 3, 4, 4, 3, 3, 3, 4, 4, 3, 4, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 3, 2, 4, 3, 3, 2, 4, 3, 4, 4, 4, 2, 3, 3, 3, 4, 4, 2, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 2, 3, 2, 4, 3, 4, 3, 4, 3, 4, 3, 3, 2, 3, 4, 4, 2, 4, 3, 4, 3, 3, 3, 3, 3, 3, 4, 4, 3, 4, 2, 3, 3, 4, 3, 4, 2, 2, 3, 4, 4, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 4, 3, 2, 3, 4, 2, 4, 3, 4, 3, 4, 3, 3, 4, 3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 2, 3, 3, 4, 3, 4, 3, 4, 2, 4, 3, 3, 2, 3, 4, 4, 3, 3, 3, 4, 3, 4, 3, 4, 2, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 2, 4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 4, 4, 3, 3, 4, 3, 4, 3, 4, 2, 3, 4, 4, 4, 3, 3, 3, 2, 3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 4, 3, 4, 2, 4, 3, 3, 3, 4, 3, 2, 3, 3, 3, 3, 3, 3, 3, 4, 2, 4, 3, 4, 3, 4, 2, 4, 2, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 2, 3, 3, 3, 2, 4, 2, 4, 3, 4, 3, 4, 3, 4, 3, 3, 4, 4, 2, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 2, 3, 2, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 2, 3, 3, 4, 3, 2, 3, 4, 2, 3, 4, 4, 4, 4, 2, 3, 3, 4, 3, 4, 3, 4, 3, 2, 4, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 4, 3, 4, 3, 4, 2, 2, 3, 4, 4, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 2, 4, 3, 4, 3, 4, 3, 3, 2, 3, 4, 4, 2, 4, 3, 4, 3, 4, 2, 3, 3, 3, 4, 4, 2, 3, 4, 4, 2, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 4, 3, 3, 3, 3, 3, 4, 4, 2, 3, 3, 4, 3, 4, 3, 4, 2, 3, 3, 3, 3, 3, 4, 4, 2, 3, 2, 4, 3, 3, 3, 3, 2, 4, 3, 4, 3, 4, 2, 4, 4, 4, 3, 2, 3, 3, 4, 4, 3, 3, 3, 4, 3, 2, 3, 4, 2, 3, 4, 3, 4, 4, 3, 4, 2, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 2, 3, 3, 4, 3, 4, 3, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 2, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 2, 3, 2, 4, 2, 4, 3, 3, 3, 4, 3, 3, 2, 3, 3, 4, 3, 4, 2, 2, 4, 4, 3, 3, 2, 3, 2, 4, 2, 3, 4, 3, 2, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 2, 2, 3, 4, 4, 3, 3, 2, 4, 3, 4, 3, 4, 2, 3, 2, 4, 3, 4, 2, 3, 3, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 3, 3, 3, 2, 4, 2, 4, 3, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 3, 2, 3, 2, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 2, 4, 3, 3, 3, 4, 3, 2, 2, 3, 3, 3, 3, 3, 2, 4, 4, 4, 3, 4, 2, 2, 3, 4, 3, 3, 4, 4, 2, 4, 3, 3, 3, 3, 3, 2, 3, 3, 4, 4, 3, 3, 2, 4, 3, 4, 3, 2, 3, 2, 3, 4, 4, 4, 3, 3, 2, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 3, 2, 3, 2, 4, 3, 4, 3, 4, 3, 4, 3, 4, 2, 3, 4, 4, 2, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 2, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 4, 2, 3, 3, 4, 3, 4, 3, 3, 2, 3, 4, 4, 4, 4, 3, 4, 2, 3, 3, 4, 3, 4, 2, 3, 4, 4, 3, 3, 2, 3, 3, 4, 3, 4, 2, 2, 3, 3, 4, 4, 2, 3, 2, 4, 3, 4, 3, 3, 3, 4, 3, 3, 2, 3, 4, 4, 3, 3, 3, 4, 3, 4, 3, 3, 2, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 2, 3, 3, 3, 3, 4, 2, 4, 3, 4, 3, 4, 3, 4, 3, 3, 2, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 2, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 2, 3, 4, 2, 3, 4, 4, 4, 4, 3, 3, 4, 4, 3, 2, 2, 3, 4, 4, 3, 3, 2, 4, 3, 4, 3, 3, 2, 2, 3, 4, 4, 4, 3, 4, 2, 3, 3, 3, 3, 3, 4, 4, 3, 3, 4, 4, 4, 4, 3, 4, 3, 3, 3, 2, 3, 3, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 2, 4, 3, 4, 3, 4, 2, 3, 2, 3, 2, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 2, 3, 3, 3, 3, 3, 4, 4, 2, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 2, 3, 2, 4, 3, 4, 3, 4]
    for i in range(150000,N):
        anscur = i
        cnt = 1
        while anscur != 0:
            ans2 = bin(anscur)[2:]
            oneCount = sum(map(lambda x: x == '1',ans2))
            anscur %= oneCount
            cnt += 1
        lowNumber.append(cnt)
    MOD = sum(map(lambda x: x == '1',X))
    if MOD == 0:
        print("1" + "\n1" * (N-1))
        return 0
    if MOD == 1 and X[-1] == '1':
        print("2\n" * (N-1) + "0")
        return 0
    if MOD == 1 and X[-1] == '0':
        ans = ''
        for i in range(N):
            if X[i] == '1':
                ans += '0'
            elif i != N-1:
                ans += '1'
            else:
                ans += '2'
            if i != N-1:
                ans += '\n'
        print(ans)
        return 0
    MODP1 = MOD + 1
    MODM1 = MOD - 1
    POWEROFTWOP1 = [0] * 200001
    POWEROFTWOM1 = [0] * 200001
    POWEROFTWOP1[0] = 1
    POWEROFTWOM1[0] = 1
    for i in range(1,N):
        POWEROFTWOP1[i] = (POWEROFTWOP1[i-1] * 2) % MODP1
        POWEROFTWOM1[i] = (POWEROFTWOM1[i-1] * 2) % MODM1
    xMODP1 = 0
    xMODM1 = 0
    for i in range(N):
        if X[i] == '1':
            xMODP1 += POWEROFTWOP1[N - i - 1]
            xMODP1 %= MODP1
            xMODM1 += POWEROFTWOM1[N - i - 1]
            xMODM1 %= MODM1
    ans = ""
    for i in range(N):
        if X[i] == '0':
            anscur = xMODP1
            anscur += POWEROFTWOP1[N - i - 1]
            anscur %= MODP1
        if X[i] == '1':
            anscur = xMODM1
            anscur -= POWEROFTWOM1[N - i - 1]
            anscur %= MODM1
        ans += str(lowNumber[anscur])
        if i != N-1:
            ans += '\n'
    print(ans)
                    
main()