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 Rust (1.42.0) (judge verdict: Accepted)

use std::io::Read;
use std::collections::HashMap;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    println!("{}", answer);
}

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: usize = iterator.next().unwrap().parse().unwrap();
    let s: String = iterator.next().unwrap().to_string();

    let x: Vec<isize> = s.chars().map(|c| c.to_digit(10).unwrap() as isize).collect();
    let pc: isize = x.iter().sum();

    let mut ans: Vec<isize> = vec![0; n];
    for b in 0..2 {
        let npc = if b == 0 {
            pc + 1
        } else {
            pc - 1
        };

        if npc <= 0 {
            continue;
        }

        let mut r0: isize = 0;
        for i in 0..n {
            r0 = (r0 * 2) % npc;
            r0 += x[i];
        }

        let mut k: isize = 1;
        for i in (0..n).rev() {
            if x[i] == b {
                let mut r = r0;
                if b == 0 {
                    r = (r + k) % npc;
                } else {
                    r = (r - k + npc) % npc;
                }
                ans[i] = f(r) + 1;
            }
            k = (k * 2) % npc;
        }
    }

    let mut result = String::new();
    for i in 0..n {
        result.push_str(&format!("{}\n", ans[i]));
    }
    result.trim().to_string()
}

fn f(x: isize) -> isize {
    if x == 0 {
        return 0;
    }
    return f(x % pcnt(x)) + 1;
}

fn pcnt(mut x: isize) -> isize {
    let mut cnt = 0;
    while x > 0 {
        if x % 2 == 1 {
            cnt += 1;
        }
        x /= 2;
    }
    return cnt;
}