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;

namespace AtCoder.AISing
{
    class D
    {
        static int[] f;

        private static int Popcount(int x)
        {
            x = (x & 0x5555) + (x >> 1 & 0x5555);
            x = (x & 0x3333) + (x >> 2 & 0x3333);
            x = (x & 0x0f0f) + (x >> 4 & 0x0f0f);
            return (x & 0x00ff) + (x >> 8 & 0x00ff);
        }


        public static void Main()
        {
            var n = int.Parse(Console.ReadLine());
            var x = Console.ReadLine().ToCharArray();

            var bitN = x.Count(c => c == '1');
            if (bitN == 0)
            {
                for (int i = 0; i < n; i++)
                    Console.WriteLine(1);
                return;
            }


            int xmodp = 0;
            int xmodm = 0;

            for (int i = 0; i < n; i++)
            {
                xmodp = ((xmodp << 1) + x[i] - '0') % (bitN + 1);
                xmodm = ((xmodm << 1) + x[i] - '0') % (bitN - 1);
            }

            var diffp = new int[n];
            var diffm = new int[n];
            diffp[n - 1] = 1 % (bitN + 1);
            diffm[n - 1] = 1 % (bitN - 1);
            for (int i = n - 1; i > 0; i--)
            {
                diffp[i - 1] = (diffp[i] << 1) % (bitN + 1);
                diffm[i - 1] = (diffm[i] << 1) % (bitN - 1);
            }

            f = new int[n+1];

            for (int i = 0; i < n; i++)
            {
                int y;
                if (x[i] == '1')
                    y = (xmodm - diffm[i] + (bitN - 1)) % (bitN - 1);
                else
                    y = (xmodp + diffp[i] + (bitN + 1)) % (bitN + 1);
                Console.WriteLine(CalcF(y) + 1);
            }

        }
        
        static int CalcF(int x)
        {
            if (x == 0)
                return 0;
            if (f[x] != 0)
                return f[x];

            int count = 0;
            int xx = x;
            while (xx != 0 && f[xx] == 0)
            {
                xx %= Popcount(xx);
                count++;
            }
            f[x] = count + f[xx];
            return f[x];
        }
    }
}