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)

from collections import defaultdict
N = int(input())
X = list(input())
d = defaultdict(int)

for i in range(1, N):
    c = 0
    k = format(i, "b")
    for j in k:
        if j == "1":
            c += 1
    d[i] = i % c

n = 0
for i in X:
    if i == "1":
        n += 1

p = 1
total1 = 0
total2 = 0
for i in X[::-1]:
    if i == "1":
        total1 += p % (n+1)
        total2 += p % (n-1)
    p *= 2

total1 %= (n+1)
total2 %= (n-1)
Ans = []
p = 1
for i in X[::-1]:
    c = 1
    if i == "0":
        start = total1
        start += p % (n+1)
        start %= (n+1)
    else:
        start = total2
        start -= p % (n-1)
        start += n - 1
        start %= (n-1)
    if start == 0:
        Ans.append(c)
    else:
        while(True):
            start = d[start]
            c += 1
            if start == 0:
                break
        Ans.append(c)
    p *= 2

for i in Ans[::-1]:
    print(i)