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.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace D
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var N = int.Parse(Console.ReadLine());
            var X = Console.ReadLine().Select(x => x == '1').ToArray();
            var dpc = X.Count(x => x);
            var dnWhen0 = GetValue(X, dpc + 1);
            var dnWhen1 = GetValue(X, dpc - 1);
            var answer = new int[N];
            var memo = new int[N + 1];
            for (var i = 1; i < memo.Length; i++)
            {
                memo[i] = i % PopCount(i);
            }
            var counts = new int[N + 1];
            for (var i = 1; i < counts.Length; i++)
            {
                counts[i] = counts[memo[i]] + 1;
            }

            for (var i = 0; i < X.Length; i++)
            {
                var pc = dpc;
                var n = 0;
                pc += X[i] ? -1 : 1;
                if (pc <= 0) continue;
                var pow = Power(2, N - 1 - i, pc);
                if (X[i]) n = (pc + dnWhen1 - pow) % pc;
                else n = (dnWhen0 + pow) % pc;

                Console.WriteLine(counts[n] + 1);
            }
        }

        private static int GetValue(bool[] n, int mod)
        {
            var ret = 0;
            for (var i = 0; i < n.Length; i++)
            {
                if (n[n.Length - 1 - i])
                {
                    ret += Power(2, i, mod);
                    ret %= mod;
                }
            }
            return ret;
        }

        private static int PopCount(int n)
        {
            var i = 0;
            var count = 0;
            while ((1 << i) <= n)
            {
                if (((n >> i) & 1) == 1) count++;
                i++;
            }
            return count;
        }

        public static int Power(int x, int y, int mod)
        {
            var result = 1;
            while (y > 0)
            {
                if ((y & 1) == 1) result = ((result % mod) * (x % mod)) % mod;
                x = ((x % mod) * (x % mod)) % mod;
                y >>= 1;
            }
            return result;
        }
    }
}