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: Accepted)

package main

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

func configure(scanner *bufio.Scanner) {
	scanner.Split(bufio.ScanWords)
	scanner.Buffer(make([]byte, 1000005), 1000005)
}
func getNextString(scanner *bufio.Scanner) string {
	scanned := scanner.Scan()
	if !scanned {
		panic("scan failed")
	}
	return scanner.Text()
}
func getNextInt(scanner *bufio.Scanner) int {
	i, _ := strconv.Atoi(getNextString(scanner))
	return i
}
func getNextInt64(scanner *bufio.Scanner) int64 {
	i, _ := strconv.ParseInt(getNextString(scanner), 10, 64)
	return i
}
func getNextFloat64(scanner *bufio.Scanner) float64 {
	i, _ := strconv.ParseFloat(getNextString(scanner), 64)
	return i
}
func main() {
	fp := os.Stdin
	wfp := os.Stdout
	extra := 0
	if os.Getenv("I") == "IronMan" {
		fp, _ = os.Open(os.Getenv("END_GAME"))
		extra = 100
	}
	scanner := bufio.NewScanner(fp)
	configure(scanner)
	writer := bufio.NewWriter(wfp)
	defer func() {
		r := recover()
		if r != nil {
			fmt.Fprintln(writer, r)
		}
		writer.Flush()
	}()
	solve(scanner, writer)
	for i := 0; i < extra; i++ {
		fmt.Fprintln(writer, "-----------------------------------")
		solve(scanner, writer)
	}
}
func solve(scanner *bufio.Scanner, writer *bufio.Writer) {
	n := getNextInt(scanner)
	x := getNextString(scanner)
	ones := 0
	for i := 0; i < n; i++ {
		ones += int(x[i] - '0')
	}
	if ones == 0 {
		for i := 0; i < n; i++ {
			fmt.Fprintln(writer, 1)
		}
		return
	}
	mm := calc(ones-1, n)
	pp := calc(ones+1, n)
	ms := 0
	ps := 0
	for i := 0; i < n; i++ {
		if x[n-1-i] == '0' {
			continue
		}
		ps += pp[i]
		ms += mm[i]
	}
	for i := 0; i < n; i++ {
		if x[i] == '0' {
			fmt.Fprintln(writer, 1+f(mod(ps+pp[n-1-i], ones+1)))
			continue
		}
		if ones == 1 {
			fmt.Fprintln(writer, 0)
			continue
		}
		fmt.Fprintln(writer, 1+f(mod(ms-mm[n-1-i], ones-1)))
	}
}
func mod(x, m int) int {
	x %= m
	if x < 0 {
		return x + m
	}
	return x
}
func f(x int) int {
	if x == 0 {
		return 0
	}
	p := bits.OnesCount32(uint32(x))
	return 1 + f(x%p)
}
func calc(ones, n int) []int {
	ans := make([]int, n)
	if ones == 0 {
		return ans
	}
	ans[0] = 1 % ones

	for i := 1; i < n; i++ {
		ans[i] = (ans[i-1] * 2) % ones
	}
	return ans
}