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

namespace contest_Csharp
{
    class Program
    {


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

                var vals = Console.ReadLine().Split(' ').
                    Select(x => int.Parse(x)).ToList();

                var N = vals[0];
                var X = Console.ReadLine();

                var cnt1A = X.Count(x => x == '1');
                var cnt1B = cnt1A - 1;

                //X=0,1の処理
                if (cnt1A == 0)
                {
                    for (int i = 0; i < N; i++)
                    {
                        Console.WriteLine(1);
                    }
                }
                else if (cnt1A == 1)
                {
                    for (int i = 0; i < N; i++)
                    {
                        
                        if (X[i] == '1')
                            Console.WriteLine(0);
                        else if(i==N-1)
                            Console.WriteLine(2);
                        else if (X[N - 1] == '1')
                            Console.WriteLine(2);
                        else
                            Console.WriteLine(1);
                    }
                }
                else
                {
                    cnt1A++;
                    int[] modA = new int[N];
                    int[] modB = new int[N];
                    modA[0] = 1;
                    modB[0] = 1;
                    for (int i = 1; i < N; i++)
                    {
                        modA[i] = (modA[i - 1] * 2) % cnt1A;
                        modB[i] = (modB[i - 1] * 2) % cnt1B;
                    }
                    long modAsum = 0;
                    long modBsum = 0;
                    for (int i = 0; i < N; i++)
                    {
                        if (X[N - 1 - i] == '1')
                        {
                            modAsum = (modAsum + modA[i]) % cnt1A;
                            modBsum = (modBsum + modB[i]) % cnt1B;
                        }
                    }

                    for (int i = 0; i < N; i++)
                    {
                        if (X[i] == '1')
                        {
                            int K = (int)(modBsum - modB[N - 1 - i]) % cnt1B;
                            K = (cnt1B + K) % cnt1B;
                            int ans = 1;
                            while (K != 0)
                            {
                                /*int Kp = propcnt(K);
                                if (Kp == 0)
                                {
                                    break;
                                }*/
                                K = K % propcnt(K);
                                ans++;
                            }
                            Console.WriteLine(ans);
                        }
                        if (X[i] == '0')
                        {
                            int K = (int)(modAsum + modA[N - 1 - i]) % cnt1A;
                            K = (cnt1A + K) % cnt1A;
                            int ans = 1;
                            while (K != 0)
                            {
                                
                                K = K % propcnt(K);
                                ans++;
                            }
                            Console.WriteLine(ans);
                        }
                    }


                    //var ans = A.Where((x,i)=> (x%2==1 && i%2==0)).Count();



                }
            }
            //Console.WriteLine(propcnt(8));
            Console.Out.Flush();
        }
        static public int propcnt(int n)
        {
            int result = 0;
            for (int i = 0; i < 25; i++)
            {
                result += (n >> i) % 2;
            }
            return result;
        }




    }
}