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: Wrong Answer)

using System;
class Program
{
    static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        string x = Console.ReadLine();
        int v = 0;
        for(int i = 0; i < n; i++)
        {
            if(x[n - i - 1]=='1')v += (int)Math.Pow(2, i);
        }
        for(int i=0; i < n; i++)
        {
            int temp = v;
            if (x[i] == '1') temp -= (int)Math.Pow(2, n-i-1);
            if (x[i] == '0') temp += (int)Math.Pow(2, n-i-1);
            int cnt = 0;
            while (temp > 0)
            {
                int p=Popcount(temp);
                temp %= p;
                cnt++;
            }
            Console.WriteLine(cnt);
        }
    }
    static public int Popcount(int z)
    {
        int ret = 0;
        while (z > 0)
        {
            if (z % 2 == 1) ret++;
            z /= 2;
        }
        return ret;
    }
}
//namespace C
//{
//    class Program
//    {
//        static void Main(string[] args)
//        {
//            int n = int.Parse(Console.ReadLine());
//            string x = Console.ReadLine();
//            for (int i = 0; i < n; i++)
//            {
//                int t = 0;
//                for (int j = 0; j < n; j++)
//                {
//                    int p = (int)Math.Pow(2, j);
//                    if (n - j - 1 == i)
//                    {
//                        if (x[n - j - 1] == '0') t += 1 * p;
//                    }
//                    else
//                    {
//                        if (x[n - j - 1] == '1') t += 1 * p;
//                    }
//                }
//                int cnt = 0;
//                for (; ; )
//                {
//                    int r = Popcount(t);
//                    if (r == 0) break;
//                    cnt++;
//                    t %= r;
//                }
//                Console.WriteLine(cnt);
//            }

//        }
//        static public int Popcount(int z)
//        {
//            int ret = 0;
//            while (z > 0)
//            {
//                if (z % 2 == 1) ret++;
//                z /= 2;
//            }
//            return ret;
//        }

//    }
//}