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.Text.RegularExpressions;
using static System.Console;
using static System.Math;
using static MyIO;
using static MyUtil;
using static BinaryRepresentation;

public class D { public static void Main() => (new Solver()).Solve(); }

public class Solver
{
	public void Solve()
	{
		long N = GetLong();
		var X = GetString();

		var f = new long[N];
		for(long i = N - 1; i >= 0; i--)
		{
			var tmp = X.ToCharArray();
			tmp[i] = (tmp[i] == '0') ? '1' : '0';
			long rest = Convert.ToInt64(new String(tmp), 2);
			long cnt = 0;
			while(rest != 0)
			{
				rest = rest % popcnt(rest);
				cnt++;
			}
			f[i] = cnt;
		}
		WriteLine(string.Join("\n", f));
	}
}

public static class BinaryRepresentation
{
	/*
	* initialize: array = { 0, 1, 2, ..., N - 1 } 
	* do { ... } while(nextPermutarion(ref array));
	*/
	public static bool nextPermutation(ref int[] array)
	{
		int len = array.Length;
		int i = len - 2;
		while((i >= 0) && (array[i] > array[i + 1]))
			i--;
		if(i < 0)
			return false;

		int pivot = array[i];
		int j = i + 1;
		while((j < len - 1) && (array[j + 1] > pivot))
			j++;
		
		int tmp = array[i];
		array[i] = array[j];
		array[j] = tmp;
		
		Array.Reverse(array, i + 1, len - i - 1);

		return true;
	}

	/* 
	* nCk
	* initialize: comb = (1 << k) - 1
	* while(comb < (1 << n)) { ...; comb = nextCombination(comb); };
	*/
	public static int nextCombination(int comb)
	{
		int x = comb & -comb;
		int y = comb + x;
		return (((comb & ~y) /x) >> 1) | y;
	}

	public static int popcnt(int v) {
		v = v - ((v >> 1) & 0x55555555);
		v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
		return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
	}

	public static long popcnt(long v) {
		v = v - ((v >> 1) & 0x5555555555555555);
		v = (v & 0x3333333333333333) + ((v >> 2) & 0x3333333333333333);
		return ((v + (v >> 4) & 0xF0F0F0F0F0F0F0F) * 0x101010101010101) >> 56;
	}
}

public static class MyIO
{
	private static string[] args = new string[0];
	private static int cnt = 0;
	private static IEnumerable<string> getArgs(long N) => Range(0, N).Select(_ => getArg());
	private static string getArg()
	{
		if(cnt == args.Length) { args = Console.ReadLine().Split(); cnt = 0; }
		return args[cnt++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static decimal GetDecimal() => decimal.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(long N) => getArgs(N).Select(int.Parse).ToArray();
	public static long[] GetLongs(long N) => getArgs(N).Select(long.Parse).ToArray();
	public static double[] GetDoubles(long N) => getArgs(N).Select(double.Parse).ToArray();
	public static decimal[] GetDecimals(long N) => getArgs(N).Select(decimal.Parse).ToArray();
	public static string[] GetStrings(long N) => getArgs(N).ToArray();
}

public static class MyUtil
{
	public static void chmax<T>(ref T x, T y) where T : IComparable<T> { if(x.CompareTo(y) < 0) x = y; }
	public static void chmin<T>(ref T x, T y) where T : IComparable<T> { if(x.CompareTo(y) > 0)	x = y; }
	public static void swap<T>(ref T x, ref T y) { T tmp = x; x = y; y = tmp; }
	public static long rightShift(long x, long y) => (x >> (int)y);
	public static long leftShift(long x, long y) => (x << (int)y);
	public static bool contains(long s, long x) => (rightShift(s, x) & 1L) == 1L;
	public static long gcd(long x, long y) => (y == 0) ? x : gcd(y, x % y);
	public static long lcm(long x, long y) => (x / gcd(x,y)) * y;	
	public static IEnumerable<int> Range(long start, long count) => Enumerable.Range((int)start, (int)count);
	public static void Sort(this List<string> source) => source.Sort(StringComparer.Ordinal);
}