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 Go (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"fmt"
	"math/bits"
	"strconv"
)

func popCount(n uint64) int {
	return bits.OnesCount64(n)
}

func f(n int64) int {
	cnt := 0
	for n != 0 {
		n = n % int64(popCount(uint64(n)))
		cnt++
	}
	
	return cnt
}

func bitFlip(n int64, pos int) int64 {
	return n ^ (int64(1) << pos)
}

func solve(n uint, s string) []int {
	answer := make([]int, 0, n)
	x, _ := strconv.ParseInt(s, 2, 64)
	
	for i := n-1; i > 0; i-- {
		xi := bitFlip(x, int(i))
		answer = append(answer, f(xi))
	}

	return answer
}

func main() {
	var N uint
	fmt.Scan(&N)

	var s string
	fmt.Scan(&s)
	

	result := solve(N, s)
	for _, n := range result {
		fmt.Println(n)
	}
}