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;
class Program
{

    static void Main(string[] args)
    {

        //var NX = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        //var L = long.Parse(Console.ReadLine());
        Solve();
        

    }

    static void Solve()
    {
        //var NM = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        var N = long.Parse(Console.ReadLine());
        var X = Console.ReadLine();

        var SumOne = 0;
        for (int i = 0; i < N; i++)
        {
            if (X[i] == '1') SumOne++;
        }
        var ReverseOne = SumOne - 1;
        var ReverseZro = SumOne + 1;

        long ReverseOneSum = 0;
        long ReverseZroSum = 0;
        for (int i = (int)N - 1; i >= 0; i--)
        {
            if (X[i] == '1') ReverseOneSum += Pow(2,(N - 1 - i), ReverseOne);
            //ReverseOneSum %= ReverseOne;
        }

        for (int i = (int)N - 1; i >= 0; i--)
        {
            if (X[i] == '1') ReverseZroSum += Pow(2,(N - 1 - i), ReverseZro);
            //ReverseZroSum %= ReverseZro;
        }

        //for (int i = (int)N - 1; i >= 0; i--)
        //{
        //    if (X[i] == '1')
        //    {
        //        var tmp = ReverseOneSum - Pow(2, (N - 1 - i), ReverseOne);
        //        tmp %= ReverseOne;
        //        Console.WriteLine(Cul(tmp,1));
        //    }
        //    else
        //    {
        //        var tmp = ReverseZroSum - Pow(2, (N - 1 - i), ReverseZro);
        //        tmp %= ReverseZro;
        //        Console.WriteLine(Cul(tmp, 1));
        //    }
        //}

        for (int i = 0; i < N; i++)
        {
            if (X[i] == '1')
            {
                var tmp = ReverseOneSum - Pow(2, (N - 1 - i), ReverseOne);
                tmp %= ReverseOne;
                Console.WriteLine(Cul(tmp, 1));
            }
            else
            {
                var tmp = ReverseZroSum + Pow(2, (N - 1 - i), ReverseZro);
                tmp %= ReverseZro;
                Console.WriteLine(Cul(tmp, 1));
            }
        }

        
        
    }

    static long Cul(long num,long count)
    {
        if(num == 0)
        {
            return count;
        }
        else
        {
            var str = Convert.ToString(num, 2);
            var countone = 0;
            for (int i = 0; i < str.Length; i++)
            {
                if (str[i] == '1') countone++;
            }

            return Cul(num % countone, count + 1);
        }
    }

    static long Pow(long n, long p, int mod = (int)1e9 + 7)
    {
        if (p == 0) return 1; // nの0乗は1
        else if (p % 2 == 0)
        {
            var x = Pow(n, p / 2, mod);
            return (x * x) % mod;
        }
        else
        {
            return Pow(n, p - 1, mod) * n % mod;
        }
    }
}