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.BufferedReader;
// import java.io.FileInputStream;
// import java.io.FileOutputStream;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.IOException;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.util.TreeSet;

import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.util.Arrays.fill;
import static java.util.Collections.sort;

public class Main {
    private FastScanner in;
    private PrintWriter out;

    private void solve() throws IOException {
        int n = in.nextInt();
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = in.nextLong();
        }

        long[][] xor = new long[n][n];
        long[][] ans = new long[n][n];
        for (int i = 0; i < n; i++) {
            if (i == 0) {
                for (int j = 0; j < n; j++) {
                    ans[i][j] = xor[i][j] = a[j];
                }
            } else {
                for (int j = 0; j < n - i; j++) {
                    ans[i][j] = max(xor[i][j] = xor[i - 1][j] ^ xor[i - 1][j + 1], max(ans[i - 1][j], ans[i - 1][j + 1]));
                }
            }
        }

        int q = in.nextInt(), l, r;
        while (q-- > 0) {
            l = in.nextInt() - 1;
            r = in.nextInt() - 1;
            out.println(ans[r - l][l]);
        }
    }

    class FastScanner {
        StringTokenizer st;
        BufferedReader br;

        FastScanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        boolean hasNext() throws IOException {
            return br.ready() || (st != null && st.hasMoreTokens());
        }

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

        long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        double nextDouble() throws IOException {
            return Double.parseDouble(next().replace(',', '.'));
        }

        String nextLine() throws IOException {
            return br.readLine();
        }

        boolean hasNextLine() throws IOException {
            return br.ready();
        }

    }

    private void run() throws IOException {
        in = new FastScanner(System.in); // new FastScanner(new FileInputStream(".in"));
        out = new PrintWriter(System.out); // new PrintWriter(new FileOutputStream(".out"));

        solve();

        out.flush();
        out.close();
    }

    public static void main(String[] args) throws IOException {
        new Main().run();
    }
}
