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.Text;
using System.Collections.Generic;
using System.Collections;
using System.Linq;
using E = System.Linq.Enumerable;
using System.Runtime.InteropServices.ComTypes;

class Program
{
    static char[] abc = "abcdefghijklmnopqrstuvwxyz".ToCharArray();
    static long mod = 1000000007;
    static long[] ans;
    static SortedDictionary<string, long> dic = new SortedDictionary<string, long>();
    static void Main(string[] args)
    {
        //var HWK = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        var N = int.Parse(Console.ReadLine());
        var X = Console.ReadLine();
        ans = new long[2000000];
        for (int i = N -1; i >= 0; i--)
        {
            var Y = Convert.ToInt64(X, 2);
            if(X[N-1-i] == '0')
            {
                Y += (long)Math.Pow(2, i);
            }
            else
            {
                Y -= (long)Math.Pow(2, i);
            }
            Console.WriteLine(Cul(Y));
        }
        
    }


    static long Cul(long inp)
    {
        if(inp == 0)
        {
            return 0;
        }

        var binary = Convert.ToString(inp, 2);
        if (dic.ContainsKey(binary))
        {
            return dic[binary];
        }
        else
        {
            
            var count = 0;
            for (int i = 0; i < binary.Length; i++)
            {
                if (binary[i] == '1') count++;
            }
            dic.Add(binary, Cul(inp % count) + 1);
            return dic[binary];
        }
    }
}