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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.IOException;
import java.math.BigInteger;

public class Main {
    public static void main(String[] args) {
        StringBuilder builder = new StringBuilder();
        int n = readInt(builder);
        read(builder);
        BigInteger x = new BigInteger(builder.toString(), 2);

        for (int i = 0; i < n; i++) {
            BigInteger xi = x.flipBit(n - i);
            if (xi.equals(BigInteger.ZERO)) {
                System.out.println(0);
                continue;
            }

            int popcount = xi.bitCount();
            int f = xi.mod(BigInteger.valueOf(popcount)).intValue();

            if (f == 0) {
                System.out.println(1);
                continue;
            }

            int count = 2;
            while ((f = f(f)) != 0) count++;
            System.out.println(count);
        }
    }

    private static int f(int num) {
        int popcount = Integer.bitCount(num);
        return num % popcount;
    }



    private static StringBuilder read(StringBuilder builder) {
        builder.setLength(0);
        while (true) {
            try {
                int b = System.in.read();
                if (b == ' ' || b == '\n' || b == -1) {
                    break;
                } else {
                    builder.appendCodePoint(b);
                }
            } catch (IOException e) {
                break;
            }
        }

        return builder;
    }

    private static int readInt(StringBuilder builder) {
        read(builder);
        return Integer.parseInt(builder.toString());
    }

    private static int readInt(StringBuilder builder, int radix) {
        read(builder);
        return Integer.parseInt(builder.toString(), radix);
    }

    private static long readLong(StringBuilder builder) {
        read(builder);
        return Long.parseLong(builder.toString());
    }

    private static long readLong(StringBuilder builder, int radix) {
        read(builder);
        return Long.parseLong(builder.toString(), radix);
    }

    private static BigInteger readBigInteger(StringBuilder builder) {
        read(builder);
        return new BigInteger(builder.toString());
    }

    private static BigInteger readBigInteger(StringBuilder builder, int radix) {
        read(builder);
        return new BigInteger(builder.toString(), radix);
    }

    private static void skipLine() {
        while (true) {
            try {
                int b = System.in.read();
                if (b == '\n' || b == -1) {
                    break;
                }
            } catch (IOException e) {
                break;
            }
        }
    }

    private static void skip() {
        while (true) {
            try {
                int b = System.in.read();
                if (b == ' ' || b == '\n' || b == -1) break;
            } catch (IOException e) {
                break;
            }
        }
    }
}