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# (Mono-csc 3.5.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Text;
using static System.Console;
using static System.Math;

namespace Atcoder
{
    class Program
    {
        static StreamWriter sw = new StreamWriter(OpenStandardOutput()) { AutoFlush = false };
        static void Main(string[] args)
        {
            try
            {
                SetOut(sw);
                Solve.Answer();
                Out.Flush();
            }
            catch (Exception ex)
            {
                WriteLine(ex.ToString());
            }
        }
    }

    public class Solve
    {
        public static void Answer()
        {
            var N = IO.RInt;
            var X = ReadLine().Reverse().ToArray();

            var pcount = X.Count(c => c == '1');
            var pc = new int[2];
            pc[0] = pcount + 1;
            pc[1] = pcount - 1;
            if (pc[1] == 0) pc[1] = 1;

            var v = new long[2];

            var pow = new long[N, 2];
            pow[0, 0] = 1;
            pow[0, 1] = 1;
            for (int i = 0; i < N; i++)
            {
                for (int j = 0; j < 2; j++)
                {
                    if (i > 0)
                    {
                        pow[i, j] = pow[i - 1, j] * 2;
                        pow[i, j] %= pc[j];
                    }
                    if (X[i] == '1') v[j] += pow[i, j];
                    v[j] %= pc[j];
                }
            }

            for (int i = N - 1; i >= 0; i--)
            {
                if (pcount == 1 && X[i] == '1')
                {
                    WriteLine(0);
                    continue;
                }

                var j = X[i] - '0';
                var now = v[j];

                if (X[i] == '0')
                {
                    now += pow[i, j];
                    now %= pc[j];
                }
                else
                {
                    now -= pow[i, j];
                    if (now < 0) now += pc[j];
                }

                var ans = 1L;
                while (now > 0)
                {
                    ans++;
                    now %= PopCount((int)now);
                }
                WriteLine(ans);
            }
        }

        public static int PopCount(int n)
        {
            // 2^18 >= 200000
            var count = 0;
            for (int i = 0; i < 32; i++)
            {
                if (((n >> i) & 1) == 1) count++;
            }
            return count;
        }
    }

    public class IO
    {
        #region Input
        public static int RInt => int.Parse(ReadLine());
        public static long RLong => long.Parse(ReadLine());
        public static double RDouble => double.Parse(ReadLine());

        public static string[] RSString => ReadLine().Split();
        public static int[] RSInt => ReadLine().Split().Select(s => int.Parse(s)).ToArray();
        public static long[] RSLong => ReadLine().Split().Select(s => long.Parse(s)).ToArray();
        public static double[] RSDouble => ReadLine().Split().Select(s => double.Parse(s)).ToArray();
        #endregion

        #region Output
        public static void OutJoinSpace<T>(IEnumerable<T> list) => WriteLine(string.Join(" ", list));
        public static void WriteLineYes_or_No(bool flag) => WriteLine(flag ? "Yes" : "No");
        public static void WriteLineYES_or_NO(bool flag) => WriteLine(flag ? "YES" : "NO");
        #endregion
    }

    public class Mod
    {
        #region
        private readonly static long M = 1000000007;

        public static long Add(long a, long b) => (a * b) % M;
        public static long Sub(long a, long b) => (a - b) % M >= 0 ? (a - b) % M : (a - b) % M + M;
        public static long Multi(long a, long b) => (a * b) % M;
        #endregion
    }
}