For an array b of length m we define the function f as 

 f(b) = \begin{cases} b[1] &   if  m = 1 \\\ f(b[1] ⊕ b[2],b[2] ⊕ b[3],...,b[m-1] ⊕ b[m]) &   otherwise, \end{cases}  

where ⊕ is [bitwise exclusive OR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).

For example, f(1,2,4,8)=f(1⊕2,2⊕4,4⊕8)=f(3,6,12)=f(3⊕6,6⊕12)=f(5,10)=f(5⊕10)=f(15)=15

You are given an array a and a few queries. Each query is represented as two integers l and r. The answer is the maximum value of f on all continuous subsegments of the array a_l, a_{l+1}, …, a_r.

Input

The first line contains a single integer n (1 ≤ n ≤ 5000) — the length of a.

The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 2^{30}-1) — the elements of the array.

The third line contains a single integer q (1 ≤ q ≤ 100 000) — the number of queries.

Each of the next q lines contains a query represented as two integers l, r (1 ≤ l ≤ r ≤ n).

Output

Print q lines — the answers for the queries.

Examples

Input

3
8 4 1
2
2 3
1 2


Output

5
12


Input

6
1 2 4 8 16 32
4
1 6
2 5
3 4
1 2


Output

60
30
12
3

Note

In first sample in both queries the maximum value of the function is reached on the subsegment that is equal to the whole segment.

In second sample, optimal segment for first query are [3,6], for second query — [2,5], for third — [3,4], for fourth — [1,2].
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.Reader;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

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

    static class TaskD {
        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            StringBuilder sb = new StringBuilder();
            int n = in.nextInt();
            int[][] pyramid = new int[n][n];
            for (int i = 0; i < n; i++) {
                pyramid[0][i] = in.nextInt();
            }

            for (int i = 0; i < n - 1; i++) {//for each row
                for (int j = 0; j < n - 1; j++) {//for each column {
                    pyramid[i + 1][j] = pyramid[i][j] ^ pyramid[i][j + 1];
//                System.out.print(pyramid[i][j]  + " ");
                }
//            System.out.print(pyramid[i][n - 1]);
//            System.out.println("");

            }
//        System.out.println(pyramid[n - 1][0]);


            for (int i = 0; i < n - 1; i++) {//for each row
                for (int j = 0; j < n - 1; j++) {//for each column {
                    pyramid[i + 1][j] = Integer.max(pyramid[i + 1][j], pyramid[i][j]);
                    pyramid[i + 1][j] = Integer.max(pyramid[i + 1][j], pyramid[i][j + 1]);
//                System.out.print(pyramid[i][j]  + " ");
                }
//            System.out.print(pyramid[i][n - 1]);
//            System.out.println("");

            }
//        System.out.println(pyramid[n - 1][0]);

            int q = in.nextInt();
            for (int i = 0; i < q; i++) {
                int l = in.nextInt() - 1;
                int r = in.nextInt() - 1;

                sb.append(pyramid[r - l][l] + "\n");
            }
            out.print(sb);
        }

    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }

        public FastScanner(InputStream in) {
            this(new InputStreamReader(in));
        }

        public String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

    }
}

