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.Numerics;
using System.Globalization;
namespace AISing.Problems
{
    class D
    {
        static void Main()
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            int[] pc = new int[200001];
            for (int d = 0; d <= 200000; d++)
            {
                int cnt = 0;
                int m = d;
                while (m != 0)
                {
                    if (m % 2 == 1) cnt++;
                    m /= 2;
                }
                pc[d] = cnt;
            }
            int n = int.Parse(Console.ReadLine());
            char[] cs = Console.ReadLine().ToCharArray();
            int cntOne = 0;
            BigInteger y = new BigInteger(0);
            foreach (var c in cs)
            {
                y = BigInteger.Multiply(y, 2);
                if (c == '1')
                {
                    y = BigInteger.Add(y, 1);
                    cntOne++;
                }
            }
            for (int i = 0; i < n; i++) {
                BigInteger xx = y;
                if (cs[i] == '0')
                {
                    xx += BigInteger.Pow(2, n - i - 1);
                    cs[i] = '1';
                    cntOne++;
                }
                else
                {
                    xx -= BigInteger.Pow(2, n - i - 1);
                    cs[i] = '0';
                    cntOne--;
                }
                int res = 1;
                xx %= cntOne;
                int x = int.Parse(xx.ToString());
                while (x != 0)
                {
                    res++;
                    x = x % pc[x];
                }
                Console.WriteLine(res);
                if (cs[i] == '0')
                {
                    cs[i] = '1';
                    cntOne++;
                }
                else
                {
                    cs[i] = '0';
                    cntOne--;
                }
            }
            Console.Out.Flush();
        }
    }
}