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"
	"strconv"
)

func main() {
	var n int
	fmt.Scan(&n)
	var x string
	fmt.Scan(&x)
	
	a := makeArray(n, x)
	for _, v := range a {
		fmt.Println(f(v))
	}
}

func makeArray(n int, x string) (a []int64) {
	for i := 0; i < n; i++ {
		tempX := ""
		if x[i:i+1] == "0" {
			if i + 1 != n {
				tempX = x[:i] + "1" + x[i+1:]
			} else {
				tempX = x[:i] + "1"
			}
		} else {
			if i + 1 != n {
				tempX = x[:i] + "0" + x[i+1:]
			} else {
				tempX = x[:i] + "0"
			}
		}

		i, _ := strconv.ParseInt(tempX, 2, 64)
		a = append(a, i)
	}
	return a
}

func popCount(n int64) (c int64) {
	for n != 0 {
		if n % 2 == 1 {
			c++
		}
		n = n / 2
	}
	return c
}

func f(n int64) (cc int64) {
	c := popCount(n)
	for n != 0 {
		cc++
		n = n % c
		c = popCount(n % c)
	}
	if n != 0 {
		cc++
	}
	return cc
}