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;

public class Hello
{
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine().Trim());
        var s = Console.ReadLine().Trim();
        getAns(n, s);
    }
    static void getAns(int n, string s)
    {
        var s1 = n - s.Replace("1", "").Length;
        var r0 = new int[n];
        var r1 = new int[n];
        var r0mod = s1 - 1;
        var r1mod = s1 + 1;
         r0[0] = 1 % r0mod; r1[0] = 1 % r1mod;
        for (int i = 1; i < n; i++)
        {
            r0[i] = (r0[i - 1] * 2) % r0mod;
            r1[i] = (r1[i - 1] * 2) % r1mod;
        }
        var smr0 = 0;
        var smr1 = 0;
        for (int i = 0; i < n; i++)
        {
            if (s[n - 1 - i] == '1')
            {
                smr0 += r0[i];
                smr0 %= r0mod;
                smr1 += r1[i];
                smr1 %= r1mod;
            }
        }
        int res;
        for (int i = 0; i < n; i++)
        {
            if (s[i] == '1')
            {
                var targ = smr0 - r0[n - 1 - i];
                if (targ < 0) targ += r0mod;
                targ %= r0mod;
                res = f(targ);
            }
            else
            {
                var targ = smr1 + r1[n - 1 - i];
                targ %= r1mod;
                res = f(targ) ;
            }
            Console.WriteLine(res + 1);
        }
    }
    static int f(long a)
    {
        var count = 0;
        var p = a;
        while (p > 0)
        {
            p %= bitCount((ulong)p);
            count++;
        }
        return count;
    }
    static int bitCount(ulong bits)
    {
        bits = (bits & 0x5555555555555555) + (bits >> 1 & 0x5555555555555555);
        bits = (bits & 0x3333333333333333) + (bits >> 2 & 0x3333333333333333);
        bits = (bits & 0x0f0f0f0f0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f0f0f0f0f);
        bits = (bits & 0x00ff00ff00ff00ff) + (bits >> 8 & 0x00ff00ff00ff00ff);
        bits = (bits & 0x0000ffff0000ffff) + (bits >> 16 & 0x0000ffff0000ffff);
        return (int)(bits & 0x00000000ffffffff) + (int)(bits >> 32);
    }
}