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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Numerics;
public class MainClass
{
	public const long Giri = 1000000007;
	public const long DpInf = 99999999999999;
	
	public static void Main(string[] args)
	{
		var n = Console.ReadLine().ToInt();
		var x = Console.ReadLine();
		
		var dp = new long[2*100000+1];
		for(int i = 1; i < dp.Length; i++)
		{
			int q = Popcount(i);
			int m = (i % q);
			if(m == 0)
			{
				dp[i] = 1;
			}
			else
			{
				dp[i] = dp[m]+1;
			}

		}
		
		
		BigInteger inp = new BigInteger(0);
		BigInteger k = new BigInteger(1);
		
		for(int i = 0; i < x.Length; i++)
		{
			if(x[x.Length-1-i] == '1')
			{
				inp += k;
			}
			k *= 2;
			
		}
		int all = 0;
		for(int i = 0; i < x.Length; i++)
		{
			if(x[i]=='1')all++;
		}
		
		int modInt = 0;
		for(int i = 0; i < 20; i++)
		{
			if((x.Length - 1 - i) >= 0)
				modInt |= ((x[x.Length - 1 - i]-'0')<<i);
		}
		for(int i = 0; i < x.Length; i++)
		{/*
			var t = inp & 1;
			if(i!=x.Length-1)
			{
				t = inp >> (x.Length -i -1);
			
				t = (1-t);
				//Console.WriteLine(t + " " + ((1 << (x.Length-i-1))-1));
				Console.WriteLine("rev"+t);
				t<<=(x.Length-i-1);
			
				t |= ((1 << (x.Length-i-1))-1) & inp;
				Console.WriteLine("kotti");
			}
			else
			{
				t = 1 - t;
				t |= inp & ((1 << x.Length)-1);
			}
			*/
			var t = inp;
			t ^= 1 << (x.Length-i-1);
			if(x[i] == '1')
			{
				int o = (int)(t%(all-1));
				//Console.WriteLine("ind"+o + "," + t);
				{
					Console.WriteLine(dp[o]+1);
				}
				//Console.WriteLine(t);
				//Console.WriteLine(all-1);
				//Console.WriteLine(dp[all-1]);
			}
			else
			{
				int o = (int)(t%(all+1));
				{
					Console.WriteLine(dp[o]+1);
				}
				//(all+1) & 
				//Console.WriteLine(all+1);
				//Console.WriteLine(dp[all+1]);
			}
		}
		
		
	}
	
	
	static int Popcount(int k)
	{
		int wa = 0;
		for(int i = 0; i < 20; i++)
		{
			if((((uint)k>>i)&1)==1)
				wa++;
		}
		return wa;
		
	}
	
	
	
	static long GCD(long a, long b)
	{
		var v = new[] { a, b };
		while (v[1] != 0) { v = new[] { v[1], v[0] % v[1] }; }
		return v[0];
	}
	public static string[] Input() { return Console.ReadLine().Split(); }
}

public static class Smarter
{
	public static int ToInt(this string str) { return int.Parse(str); }
	public static long ToLong(this string str) { return long.Parse(str); }
	public static int[] ToInt(this string[] str, int offset = 0)
	{
		var r = new int[str.Length];
		for(int i = 0; i < str.Length; i++) r[i] = str[i].ToInt() + offset;
		return r;
	}
}