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.util.*;
import java.io.*;
import java.math.*;
 
public class Main {
    static PrintWriter out;
    static Reader in;
    public static void main(String[] args) throws IOException {
        //out = new PrintWriter(new File("out.txt"));
        //PrintWriter out = new PrintWriter(System.out);
        //in = new Reader(new FileInputStream("in.txt"));
        //Reader in = new Reader();
        input_output();
        Main solver = new Main();
        solver.solve();
        out.flush();
        out.close();
 
    }
 
    static int INF = (int)2e9+5;
    static int maxn = (int)2e6+5;
    static int mod=(int)1e9+7 ;
    static int n, m, t, q, k;
    // read the editorial of the last problem (K).

    static long[] res;

    void solve() throws IOException{
        n = in.nextInt();
        int size = 1;
        for (int i = 0; i < n; i++) size = size*2;

        int[] cop = new int[size];
        int[] arr = new int[size];
        for (int i = 0; i < size; i++) {
            arr[i] = in.nextInt();
            cop[i] = arr[i];
        }

        long[] pow = new long[n+1];
        pow[0] = 1;
        for (int i = 1; i <= n; i++) pow[i] = pow[i-1]*2;

        long tmp, x;

        // calculate res: res[i] = the number of inversions if we consider each 2^i part alone.
        res = new long[n+1];
        invCount(cop, n);


        long[] rem = new long[n+1];
        for (int i = 1; i <= n; i++) {
            for (int j = 0; j < size; j+=pow[i]) {
                Map<Integer, Integer> tmpmap = new HashMap<>();
                tmp = 0;
                for (int z = j; z < j+pow[i]; z++) {
                    tmpmap.put(arr[z], tmpmap.getOrDefault(arr[z], 0)+1);
                    x = tmpmap.get(arr[z]);
                    if (x == 2) tmp += 1L;
                    else if (x > 2) tmp += ((x-1L)*x)/2L-((x-2L)*(x-1L))/2L;
                }
                rem[i] += tmp;
            }
        }

        StringBuilder myres = new StringBuilder("");
        int mm = in.nextInt();
        long ans = res[n];
        for (int i = 0; i < mm ;i++) {
            q = in.nextInt();
            if (q == 0) {
                myres.append(ans+"\n");
                continue;
            }

            tmp = ((pow[q]-1)*pow[q])/2L;
            tmp = tmp*pow[n-q];
            ans += tmp-2L*res[q]-rem[q];
            for (int j = q+1; j <= n; j++) res[j] += tmp-2L*res[q]-rem[q];
            for (int j = 1; j <= q; j++) {
                tmp = ((pow[j]-1)*pow[j])/2L;
                tmp = tmp*pow[n-j];
                res[j] = tmp-res[j]-rem[j];
            }

            myres.append(ans+"\n");
        }
        out.println(myres);
    }
 
    //<>

    static long merge(int[] arr, int[] left, int[] right) {
        int i = 0, j = 0;
        long count = 0;
        while (i < left.length || j < right.length) {
            if (i == left.length) {
                arr[i+j] = right[j];
                j++;
            } else if (j == right.length) {
                arr[i+j] = left[i];
                i++;
            } else if (left[i] <= right[j]) {
                arr[i+j] = left[i];
                i++;                
            } else {
                arr[i+j] = right[j];
                count += left.length-i;
                j++;
            }
        }
        return count;
    }

    static long invCount(int[] arr, int power) {
        if (arr.length < 2)
            return 0;

        int m = (arr.length + 1) / 2;
        int left[] = Arrays.copyOfRange(arr, 0, m);
        int right[] = Arrays.copyOfRange(arr, m, arr.length);

        long cnt = invCount(left, power-1) + invCount(right, power-1) + merge(arr, left, right);
        res[power] += cnt;
        return cnt;
    }

    static class Reader {
 
        private InputStream mIs;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
    
        public Reader() {
            this(System.in);
        }
    
        public Reader(InputStream is) {
            mIs = is;
        }
    
        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
    
        }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = mIs.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }
    
        public String nextLine() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }
    
        public String next() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
    
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
    
        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
    
        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
    
        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    
        public boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
 
    }
    static void input_output() throws IOException {
        File f = new File("in.txt");
        if(f.exists() && !f.isDirectory()) { 
            in = new Reader(new FileInputStream("in.txt"));
        } else in = new Reader();
        f = new File("out.txt");
        if(f.exists() && !f.isDirectory()) {
            out = new PrintWriter(new File("out.txt"));
        } else out = new PrintWriter(System.out);
    }
}