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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Text;

class Program
{
	static void Main(string[] args)
	{
		int[] func = new int[200001];
		int[] popcount = new int[200001];
		for(int i=1; i<200001; i++)
		{
			popcount[i] = popcount[i/2] + i%2;
			int buf = i % popcount[i];
			func[i] = func[buf] + 1;
		}

		string[] input = Read();
		int n = int.Parse(input[0]);
		char[] x = Read()[0].ToCharArray();
		bool[] bit = new bool[n];
		int count1 = 0;
		for(int i=0; i<n; i++)
		{
			if(x[n-i-1]=='1')
			{
				bit[i] = true;
				count1++;
			}
		}
		int[][] amari = new int[n][];
		int[] amariBase = new int[2];
		int[] add = new int[]{-1,1};
		//if(count1<2) add[0] = 0;
		amari[0] = new int[2];
		for(int j=0; j<2; j++) amari[0][j] = 1 % Math.Max(count1 + add[j], 1);
		if(bit[0]){
		for(int j=0; j<2; j++) amariBase[j] = amari[0][j];}
		for(int i=1; i<n; i++)
		{
			amari[i] = new int[2];
			for(int j=0; j<2; j++) amari[i][j] = (amari[i-1][j] * 2) % Math.Max(count1 + add[j],1);
			if(bit[i]) for(int j=0; j<2; j++) amariBase[j] = (amariBase[j] + amari[i][j]) % Math.Max(count1 + add[j],1);
		}
		for(int i=0; i<n; i++)
		{
			int idx = n-i-1;
			int addIdx = bit[idx] ? 0 : 1;
			if(count1+add[addIdx]==0)
			{
				Write(0);
				continue;
			}
			int buf = amariBase[addIdx] + amari[idx][addIdx] * add[addIdx];
			if(buf < 0) buf += count1 + add[addIdx];
			buf = buf % (count1+add[addIdx]);
			Write(func[buf]+1);
		}
	}

	static string[] Read()
	{
		return Console.ReadLine().Split(' ');
	}

	static void Write(object o)
	{
		Console.WriteLine(o.ToString());
	}
}