Problem: Mashmokh's boss, Bimokh, didn't like Mashmokh. So he fired him. Mashmokh decided to go to university and participate in ACM instead of finding a new job. He wants to become a member of Bamokh's team. In order to join he was given some programming tasks and one week to solve them. Mashmokh is not a very experienced programmer. Actually he is not a programmer at all. So he wasn't able to solve them. That's why he asked you to help him with these tasks. One of these tasks is the following.

You have an array a of length 2n and m queries on it. The i-th query is described by an integer qi. In order to perform the i-th query you must:

  * split the array into 2n - qi parts, where each part is a subarray consisting of 2qi numbers; the j-th subarray (1 ≤ j ≤ 2n - qi) should contain the elements a[(j - 1)·2qi + 1], a[(j - 1)·2qi + 2], ..., a[(j - 1)·2qi + 2qi]; 
  * reverse each of the subarrays; 
  * join them into a single array in the same order (this array becomes new array a); 
  * output the number of inversions in the new a. 



Given initial array a and all the queries. Answer all the queries. Please, note that the changes from some query is saved for further queries.

Input

The first line of input contains a single integer n (0 ≤ n ≤ 20). 

The second line of input contains 2n space-separated integers a[1], a[2], ..., a[2n] (1 ≤ a[i] ≤ 109), the initial array.

The third line of input contains a single integer m (1 ≤ m ≤ 106). 

The fourth line of input contains m space-separated integers q1, q2, ..., qm (0 ≤ qi ≤ n), the queries.

Note: since the size of the input and output could be very large, don't use slow output techniques in your language. For example, do not use input and output streams (cin, cout) in C++.

Output

Output m lines. In the i-th line print the answer (the number of inversions) for the i-th query.

Examples

Input

2
2 1 4 3
4
1 2 0 2


Output

0
6
6
0


Input

1
1 2
3
0 1 1


Output

0
1
0

Note

If we reverse an array x[1], x[2], ..., x[n] it becomes new array y[1], y[2], ..., y[n], where y[i] = x[n - i + 1] for each i.

The number of inversions of an array x[1], x[2], ..., x[n] is the number of pairs of indices i, j such that: i < j and x[i] > x[j].

Solution (in JAVA):

Solution:
import java.io.InputStreamReader;
import java.io.IOException;
import java.io.FileReader;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.StringTokenizer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Agostinho Junior (junior94)
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskC solver = new TaskC();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskC {
	int[] a, help;
	long[][] count;

	public void solve(int testNumber, InputReader in, OutputWriter out) {
		int N = in.readInt();
		a = new int[1<<N];
		help = new int[1<<N];
		count = new long[N + 1][2];
		for (int i = 0; i < a.length; i++) {
			a[i] = in.readInt();
		}
		mergeSort(N, 0, a.length - 1);
		int m = in.readInt();
		int mask = 0;
		while (m-- > 0) {
			int q = in.readInt();
			mask ^= 1 << q;
			int set = 0;
			long ans = 0;
			for (int i = N; i > 0; i--) {
				if (((1 << i) & mask) > 0) {
					set ^= 1;
				}
				ans += count[i][set];
			}
			out.println(ans);
		}
	}

	public void mergeSort(final int bit, final int start, final int end) {
		if (start == end) {
			return;
		}
		int mid = (start + end) / 2;
		mergeSort(bit - 1, start, mid);
		mergeSort(bit - 1, mid + 1, end);
		merge(bit, start, mid, end);
	}

	public void merge(final int bit, final int start, final int mid, final int end) {
		for (int i = start; i <= end; i++) {
			help[i] = a[i];
		}
		int i = start;
		int j = mid + 1;
		int k = start;
		long inv = 0;
		long matches = 0;
		for (; i <= mid && j <= end; k++) {
			if (help[i] <= help[j]) {
				if (help[i] == help[j]) {
					matches ++;
				}
				a[k] = help[i ++];
			} else {
				a[k] = help[j ++];
				inv += mid - i + 1;
			}
		}
		while (i <= mid) {
			if (help[i] == a[mid]) {
				matches ++;
			}
			a[k ++] = help[i ++];
		}
		count[bit][0] += inv;
		count[bit][1] += 1L * (end - (mid + 1)  + 1) * (mid - start + 1) - matches - inv;
	}
}

class InputReader {
	private BufferedReader input;
	private StringTokenizer line = new StringTokenizer("");
	public InputReader() {
		this(System.in);
	}
	public InputReader(InputStream in) {
		input = new BufferedReader(new InputStreamReader(in));
	}
	public InputReader(String s) {
		try {
			input = new BufferedReader(new FileReader(s));
		} catch(IOException io) { io.printStackTrace(); System.exit(0);}
	}
	public void fill() {
		try {
			if(!line.hasMoreTokens()) line = new StringTokenizer(input.readLine());
		} catch(IOException io) { io.printStackTrace(); System.exit(0);}
	}

	public int readInt() {
		fill();
		return Integer.parseInt(line.nextToken());
	}
}

class OutputWriter {
	private PrintWriter output;
	public OutputWriter() {
		this(System.out);
	}
	public OutputWriter(OutputStream out) {
		output = new PrintWriter(out);
	}
	public OutputWriter(Writer writer) {
		output = new PrintWriter(writer);
	}

	public void println(Object o) {
		output.println(o);
	}

	public void close() {
		output.close();
	}
}