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.Threading.Tasks;

namespace AtCoder.Abc
{
    class QuestionD
    {
        public static int CountChar(string s, char c)
        {
            return s.Length - s.Replace(c.ToString(), "").Length;
        }

        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            // 文字列の入力


            // 整数の入力
            int N = int.Parse(Console.ReadLine());
            string s = Console.ReadLine();

            // 文字列配列の入力
            //string[] inputStrArray = Console.ReadLine().Split(' ');

            // 整数配列の入力
            //var inputintArray = Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();


            for(int i = 0; i < N; i++)
            {
                char[] c = s.ToCharArray();
                if (c[i] == '0') c[i] = '1';
                else c[i] = '0';

                string s1 = new string(c);
                int b = Convert.ToInt32(s1, 2);
                //Console.WriteLine(s1);
                //Console.WriteLine(b);

                //bがＸi

                //Xiの中の１の個数を数えて割る作業
                int X = b;
                int cnt = 0;
                while (X > 0)
                {
                    string X2 = Convert.ToString(X, 2);
                    int cnt1 = CountChar(X2, '1');

                    X = X % cnt1;
                    cnt++;
                }
                Console.WriteLine(cnt);



            }




            Console.Out.Flush();
        }
    }
}