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)

#! /usr/bin/env python3

import sys
import numpy as np
int1 = lambda x: int(x) - 1
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(500000)

N = int(readline())
X = readline().decode().rstrip()

hoge = [pow(2, i) for i in range(N + 5)]
counts = [1 if i in hoge else -1 for i in range(N + 5)]

for i in range(N):
    cnt = X.count('1')

    tmp = 0
    X_ = list(X)
    m = 0
    if X[i] == "0":
        cnt += 1
        X_[i] = "1"
    else:
        X_[i] = "0"
        cnt -= 1

    X_ = "".join(X_)
    acc = 0
    for j, c in enumerate(X_[::-1]):
        if c == '1':
            acc += hoge[j]
    if acc > 2 * pow(10, 5):
        if acc % cnt == 0:
            print(1)
            continue
        else:
            acc %= cnt
            cnt = bin(acc).count('1')
            tmp += 1

    if counts[acc] != -1:
        print(counts[acc] + tmp)
    else:
        while True:
            if acc % cnt == 0:
                counts[acc] = 1
                print(counts[acc] + tmp)
                break
            elif counts[acc % cnt] != 0:
                counts[acc] = counts[acc % cnt] + 1
                print(counts[acc] + tmp)
                break

            acc %= cnt
            cnt = bin(acc).count('1')
            #print(acc, cnt)