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"
	"strings"
)

func getMod(X string, m int) int {

	r := 0
	for _, v := range X {
		r *= 2
		if v == '1' {
			r += 1
		}
		r %= m
	}
	return r
}

func main() {
	sc := NewScanner()
	N, X := sc.NextInt(), sc.Next()
	memo := map[int]int{}
	var dfs func(int, int) int
	dfs = func(X int, count int) int {
		if X == 0 {
			return count
		}
		if _, ok := memo[X]; !ok {
			m := bits.OnesCount32(uint32(X))
			memo[X] = dfs(X%m, count+1)
			return memo[X]
		} else {
			return memo[X] + count
		}
	}
	for i := 1; i <= N; i++ {
		dfs(i, 0)
	}
	//fmt.Printf("%+v\n", memo)

	c := strings.Count(X, "1")
	//baseMode := getMod(X, c)
	baseModePlus := getMod(X, c+1)
	var baseModeMinus int
	if c > 1 {
		baseModeMinus = getMod(X, c-1)
	} else {
		baseModeMinus = 0
	}
	ac := make([]int, 2)
	ac[0] = 1
	ac[1] = 1
	ans := make([]int, N)
	for i := N - 1; i >= 0; i-- {
		if X[i] == '0' {
			m := (baseModePlus + ac[0]) % (c + 1)
			//println(X, c, i, m, q)
			ans[i] = dfs(m, 0) + 1
		} else {
			if c == 1 {
				ans[i] = 0
			} else {
				m := (baseModeMinus - ac[1] + c - 1) % (c - 1)
				//println(baseModeMinus, ac[1], c, m)
				if m == 0 {
					ans[i] = 1
				} else {
					ans[i] = dfs(m, 0) + 1
				}
			}
		}
		for i := 0; i < 2; i++ {
			ac[i] *= 2
		}
		ac[0] %= c + 1
		if c > 1 {
			ac[1] %= c - 1
		} else {
			ac[1] = 0
		}
	}
	for i := 0; i < N; i++ {
		fmt.Println(ans[i])
	}

}

type Scanner struct {
	r   *bufio.Reader
	buf []byte
	p   int
}

func NewScanner() *Scanner {
	rdr := bufio.NewReaderSize(os.Stdin, 1000)
	return &Scanner{r: rdr}
}
func (s *Scanner) Next() string {
	s.pre()
	start := s.p
	for ; s.p < len(s.buf); s.p++ {
		if s.buf[s.p] == ' ' {
			break
		}
	}
	result := string(s.buf[start:s.p])
	s.p++
	return result
}
func (s *Scanner) NextLine() string {
	s.pre()
	start := s.p
	s.p = len(s.buf)
	return string(s.buf[start:])
}
func (s *Scanner) NextInt() int {
	v, _ := strconv.Atoi(s.Next())
	return v
}
func (s *Scanner) NextInt64() int64 {
	v, _ := strconv.ParseInt(s.Next(), 10, 64)
	return v
}

func (s *Scanner) NextFloat() float64 {
	v, _ := strconv.ParseFloat(s.Next(), 64)
	return v
}

func (s *Scanner) NextIntArray() []int {
	s.pre()
	start := s.p
	result := []int{}
	for ; s.p < len(s.buf)+1; s.p++ {
		if s.p == len(s.buf) || s.buf[s.p] == ' ' {
			v, _ := strconv.ParseInt(string(s.buf[start:s.p]), 10, 0)
			result = append(result, int(v))
			start = s.p + 1
		}
	}

	return result
}
func (s *Scanner) NextInt64Array() []int64 {
	s.pre()
	start := s.p
	result := []int64{}
	for ; s.p < len(s.buf)+1; s.p++ {
		if s.p == len(s.buf) || s.buf[s.p] == ' ' {
			v, _ := strconv.ParseInt(string(s.buf[start:s.p]), 10, 64)
			result = append(result, v)
			start = s.p + 1
		}
	}
	return result
}

func (s *Scanner) NextMap() map[int]bool {
	s.pre()
	start := s.p
	mp := map[int]bool{}
	for ; s.p < len(s.buf); s.p++ {
		if s.buf[s.p] == ' ' {
			v, _ := strconv.Atoi(string(s.buf[start:s.p]))
			mp[v] = true
			start = s.p + 1
		}
	}
	v, _ := strconv.Atoi(string(s.buf[start:s.p]))
	mp[v] = true

	return mp
}

func (s *Scanner) pre() {
	if s.p >= len(s.buf) {
		s.readLine()
		s.p = 0
	}
}
func (s *Scanner) readLine() {
	s.buf = make([]byte, 0)
	for {
		l, p, e := s.r.ReadLine()
		if e != nil {
			panic(e)
		}
		s.buf = append(s.buf, l...)
		if !p {
			break
		}
	}
}