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: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
public static class P
{
    public static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        var s = Console.ReadLine();
        var popcnt = s.Count(x => x == '1');
        BigInteger snum = 0;
        foreach (var item in s)
            snum = snum * 2 + (item - '0');
        var remainwp1 = (int)(snum % (popcnt + 1));
        var remainwm1 = (int)(popcnt <= 1 ? -1 : snum % (popcnt - 1));

        var remainswp1 = new int[n + 1];
        remainswp1[0] = 1;
        var remainswm1 = new int[n + 1];
        remainswm1[0] = popcnt <= 1 ? 0 : 1;
        for (int i = 1; i <= n; i++)
        {
            remainswp1[i] = (remainswp1[i - 1] * 2) % (popcnt + 1);
            if (popcnt > 1) remainswm1[i] = (remainswm1[i - 1] * 2) % (popcnt - 1);
        }

        static int Solve(int n) => n == 0 ? 0 : Solve(n % PopCount(n)) + 1;
        for (int i = 0; i < n; i++)
        {
            if (s[i] == '1')
            {
                if (popcnt <= 1)
                {
                    Console.WriteLine(0);
                    continue;
                }
                var remain = remainwm1 + (popcnt - 1) - remainswm1[n - i - 1];
                if (remain >= (popcnt - 1)) remain -= (popcnt - 1);
                Console.WriteLine(Solve(remain) + 1);
            }
            else
            {
                var remain = remainwp1 + remainswp1[n - i - 1];
                if (remain >= (popcnt + 1)) remain -= popcnt + 1;
                Console.WriteLine(Solve(remain) + 1);
            }
        }
    }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    static int PopCount(int n)
    {
        int msb = 0;
        if (n < 0) { n &= int.MaxValue; msb = 1; }
        n = n - ((n >> 1) & 0x55555555);
        n = (n & 0x33333333) + ((n >> 2) & 0x33333333);
        return (int)(((n + (n >> 4) & 0xF0F0F0F) * 0x1010101) >> 24) + msb;
    }
}