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 (
	"bufio"
	"fmt"
	"io"
	"os"
	"strconv"
	"strings"
)

func popcount(n int) int {
	var cnt int
	for ; n > 0; n >>= 1 {
		if n&1 == 1 {
			cnt++
		}
	}
	return cnt
}

func f(n int) int {
	return n % popcount(n)
}

func solve() {
	sc := newScanner(os.Stdin)
	n := sc.scanInt()
	x := sc.scanString()
	xcnt := strings.Count(x, "1")
	xmin, xplus := 0, 0
	xminarr := make([]int, n)
	xplusarr := make([]int, n)
	for i := 0; i < n; i++ {
		if x[i] == '0' {
			continue
		}
		if xcnt-1 > 0 {
			xmin += pow(2, n-i-1) % (xcnt - 1)
			xmin %= (xcnt - 1)
		}
		xplus += pow(2, n-i-1) % (xcnt + 1)
		xplus %= (xcnt + 1)
	}
	for i := 0; i < n; i++ {
		if xcnt-1 > 0 {
			xminarr[i] = pow(2, n-i-1) % (xcnt - 1)
		}
		xplusarr[i] = pow(2, n-i-1) % (xcnt + 1)
	}
	for i := 0; i < n; i++ {
		cnt := 1
		var y int
		if x[i] == '1' {
			if xcnt-1 == 0 {
				fmt.Println(0)
				continue
			}
			y = (xmin - xminarr[i] + xcnt - 1) % (xcnt - 1)
		} else {
			y = (xplus + xplusarr[i]) % (xcnt + 1)
		}
		for y > 0 {
			// fmt.Println(y, "ye")
			y = f(y)
			cnt++
		}
		fmt.Println(cnt)
	}
	return
}

var sc = bufio.NewScanner(os.Stdin)

type scanner struct {
	sc *bufio.Scanner
}

func newScanner(input io.Reader) *scanner {
	sc := bufio.NewScanner(input)
	sc.Split(bufio.ScanWords)
	sc.Buffer(make([]byte, 1024), int(1e+9))
	return &scanner{sc}
}

func (s *scanner) scanString() string {
	s.sc.Scan()
	return s.sc.Text()
}
func (s *scanner) scanInt() int {
	a, err := strconv.Atoi(s.scanString())
	if err != nil {
		fmt.Println(err)
	}
	return a
}
func (s *scanner) scanFloat64() float64 {
	f, err := strconv.ParseFloat(s.scanString(), 64)
	if err != nil {
		fmt.Println(err)
	}
	return f
}
func Permute(nums []int) [][]int {
	n := factorial(len(nums))
	ret := make([][]int, 0, n)
	permute(nums, &ret)
	return ret
}
func permute(nums []int, ret *[][]int) {
	*ret = append(*ret, makeCopy(nums))

	n := len(nums)
	var i, j int
	for {
		for i = n - 2; i >= 0; i-- {
			if nums[i] < nums[i+1] {
				break
			}
		}
		if i < 0 {
			return
		}
		for j = n - 1; ; j-- {
			if nums[j] > nums[i] {
				break
			}
		}
		nums[i], nums[j] = nums[j], nums[i]
		for k, l := i+1, n-1; k < l; {
			nums[k], nums[l] = nums[l], nums[k]
			k++
			l--
		}
		*ret = append(*ret, makeCopy(nums))
	}
}

func factorial(n int) int {
	ret := 1
	for i := 2; i <= n; i++ {
		ret *= i
	}
	return ret
}

func pow(n, m int) int {
	ret := 1
	for i := 0; i < m; i++ {
		ret *= n
	}
	return ret
}

func makeCopy(nums []int) []int {
	return append([]int{}, nums...)
}
func gcd(a int, b int) int {
	if b == 0 {
		return a
	}
	return gcd(b, a%b)
}

func eratosthenes(n int) []int {
	search := make([]bool, n+1)
	ans := []int{}
	for i := 2; i < n+1; i++ {
		search[i] = true
	}
	for i := 2; i*i < n+1; i++ {
		for j := 2; i*j < n+1; j++ {
			search[i*j] = false
		}
	}
	for i := 2; i < n; i++ {
		if search[i] {
			ans = append(ans, i)
		}
	}
	return ans
}

func main() {
	sc.Split(bufio.ScanWords)
	solve()
}