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: Runtime Error)


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.UncheckedIOException;
import java.lang.reflect.Array;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.Deque;
import java.util.Objects;
import java.util.regex.Pattern;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class Main {
    public void exec() {
        int n = stdin.nextInt();
        String x = stdin.nextString();

        long c = IntStream.range(0, n).filter(i -> x.charAt(i) == '1').count();
        long p1 = 0;
        long p2 = 0;
        for (int i = 0; i < n; i++) {
            if (x.charAt(i) == '1') {
                p1 += MathUtils.modPow(2, n-i-1, c+1);
                p2 += MathUtils.modPow(2, n-i-1, c-1);
                p1 %= c+1;
                p2 %= c-1;
            }
        }


        for (int i = 0; i < n; i++) {
            if (x.charAt(i) == '1') {
                long q = p2 - MathUtils.modPow(2, n-i-1, c-1);
                if (q < 0) q += c-1;
                stdout.println(f(q));
            } else {
                long q = p1 + MathUtils.modPow(2, n-i-1, c+1);
                q %= c+1;
                stdout.println(f(q));
            }
        }
    }

    public int f(long n) {
        if (n==0) {
            return 1;
        }
        return f(n%Long.bitCount(n))+1;
    }

    private static class MathUtils {
        private MathUtils() {}

        public static long modPow(long x, long y, long mod) {
            long z = 1;
            while (y > 0) {
                if (y % 2 == 0) {
                    x = (x * x) % mod;
                    y /= 2;
                } else {
                    z = (z * x) % mod;
                    y--;
                }
            }
            return z;
        }

        public static long modInv(long x, long mod) {
            return modPow(x, mod - 2, mod);
        }
    }

    private static final Stdin stdin = new Stdin();
    private static final Stdout stdout = new Stdout();

    public static void main(String[] args) {
        new Main().exec();
        stdout.flush();
    }

    public static class Stdin {
        private BufferedReader stdin;
        private Deque<String> tokens;
        private Pattern delim;

        public Stdin() {
            stdin = new BufferedReader(new InputStreamReader(System.in));
            tokens = new ArrayDeque<>();
            delim = Pattern.compile(" ");
        }

        public String nextString() {
            try {
                if (tokens.isEmpty()) {
                    String line = stdin.readLine();
                    delim.splitAsStream(line).forEach(tokens::addLast);
                }
                return tokens.pollFirst();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public int nextInt() {
            return Integer.parseInt(nextString());
        }

        public double nextDouble() {
            return Double.parseDouble(nextString());
        }

        public long nextLong() {
            return Long.parseLong(nextString());
        }

        public String[] nextStringArray(int n) {
            String[] a = new String[n];
            for (int i = 0; i < n; i++) a[i] = nextString();
            return a;
        }

        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        public double[] nextDoubleArray(int n) {
            double[] a = new double[n];
            for (int i = 0; i < n; i++) a[i] = nextDouble();
            return a;
        }

        public long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }
    }

    public static class Stdout {
        private PrintWriter stdout;

        public Stdout() {
            stdout =  new PrintWriter(System.out, false);
        }

        public void printf(String format, Object ... args) {
            stdout.printf(format, args);
        }

        public void println(Object ... objs) {
            String line = Arrays.stream(objs).map(this::deepToString).collect(Collectors.joining(" "));
            stdout.println(line);
        }

        private String deepToString(Object o) {
            if (o == null || !o.getClass().isArray()) {
                return Objects.toString(o);
            }

            int len = Array.getLength(o);
            String[] tokens = new String[len];
            for (int i = 0; i < len; i++) {
                tokens[i] = deepToString(Array.get(o, i));
            }
            return "{" + String.join(",", tokens) + "}";
        }

        public void flush() {
            stdout.flush();
        }
    }
}