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: Runtime Error)

package main

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

func main() {
	N := getStdinInt64()
	X := getStdin()

	var i int64 = 0
	var bits int64 = 0
	var n int64 = 0
	for i = int64(len(X)) - 1; i >= 0; i-- {
		if X[i] == '1' {
			bits += 1 << n
		}
		n++
	}

	fInit(1 << (N + 2))
	for i = 0; i < N; i++ {
		b := bits ^ (1 << (N - 1 - i))
		fmt.Printf("%d\n", f(b))
	}
}

func popcount(n int64) int {
	return bits.OnesCount64(uint64(n))
}

var mod []int64

func fInit(max int64) {
	mod = make([]int64, max+1)
	var i int64 = 0
	for i = 1; i <= max; i++ {
		pop := popcount(i)
		if pop != 0 {
			mod[i] = i % int64(pop)
		} else {
			mod[i] = 0
		}
	}
}

func f(n int64) int64 {
	if n == 0 {
		return 0
	}
	var cnt int64 = 0
	for {
		n = mod[n]
		cnt++
		if n <= 0 {
			break
		}
	}
	return cnt
}

var sc = bufio.NewReaderSize(os.Stdin, 1024*1024*10)

func getStdin() string {
	return readLine()
}
func getStdinInt() int {
	str := getStdin()
	rtn, _ := strconv.Atoi(str)
	return rtn
}
func getStdinInt2() (int, int) {
	list := getStdinIntArr()
	return list[0], list[1]
}
func getStdinInt3() (int, int, int) {
	list := getStdinIntArr()
	return list[0], list[1], list[2]
}
func getStdinInt64() int64 {
	str := getStdin()
	rtn, _ := strconv.ParseInt(str, 10, 64)
	return rtn
}
func getStdinInt64_2() (int64, int64) {
	list := getStdinIntArr64()
	return list[0], list[1]
}
func getStdinInt64_3() (int64, int64, int64) {
	list := getStdinIntArr64()
	return list[0], list[1], list[2]
}
func getStdinIntArr() []int {
	str := getStdin()
	list := strings.Split(str, " ")
	rtn := make([]int, len(list))
	for idx, val := range list {
		rtn[idx], _ = strconv.Atoi(val)
	}
	return rtn
}
func getStdinIntArr64() []int64 {
	str := getStdin()
	list := strings.Split(str, " ")
	rtn := make([]int64, len(list))
	for idx, val := range list {
		rtn[idx], _ = strconv.ParseInt(val, 10, 64)
	}
	return rtn
}
func readLine() string {
	buf := make([]byte, 0, 0)
	for {
		l, p, _ := sc.ReadLine()
		buf = append(buf, l...)
		if !p {
			break
		}
	}
	return string(buf)
}