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.IOException;
import java.io.InputStreamReader;

public class ProblemD {
    BufferedReader rd;

    ProblemD() throws IOException {
        rd = new BufferedReader(new InputStreamReader(System.in));
        compute();
    }

    private void compute() throws IOException {
        rd.readLine();
        int[] a = intarr();
        int q = pint();
        int[][] qs = new int[q][];
        for(int i=0;i<q;i++) {
            qs[i] = intarr();
        }
        int[] res = solve(a, qs);
        StringBuilder buf = new StringBuilder();
        for(int x: res) {
            if(buf.length() > 0) {
                buf.append('\n');
            }
            buf.append(x);
        }
        out(buf);
    }

    private int[] solve(int[] a, int[][] qs) {
        int n = a.length;
        int[][] p = new int[n+1][n];
        p[1] = a;
        for(int i=2;i<=n;i++) {
            for(int j=0;j<=n-i;j++) {
                p[i][j] = p[i-1][j] ^ p[i-1][j+1];
            }
        }
        int[][] dp = new int[n+1][n];
        dp[1] = p[1];
        for(int i=2;i<=n;i++) {
            for(int j=0;j<=n-i;j++) {
                dp[i][j] = max(dp[i-1][j], dp[i-1][j+1], max(p[i][j], p[i-1][j], p[i-1][j+1]));
            }
        }

        int[] res = new int[qs.length];
        for(int i=0;i<qs.length;i++) {
            int l = qs[i][0];
            int r = qs[i][1];
            res[i] = dp[r-l+1][l-1];
        }
        return res;
    }

    private int max(int a, int b, int c) {
        return Math.max(a, Math.max(b, c));
    }

    private int pint() throws IOException {
        return pint(rd.readLine());
    }

    private int pint(String s) {
        return Integer.parseInt(s);
    }

    private int[] intarr() throws IOException {
        return intarr(rd.readLine());
    }

    private int[] intarr(String s) {
        String[] q = split(s);
        int n = q.length;
        int[] a = new int[n];
        for(int i=0;i<n;i++) {
            a[i] = Integer.parseInt(q[i]);
        }
        return a;
    }

    private String[] split(String s) {
        if(s == null) {
            return new String[0];
        }
        int n = s.length();
        int start = -1;
        int end = 0;
        int sp = 0;
        boolean lastWhitespace = true;
        for(int i=0;i<n;i++) {
            char c = s.charAt(i);
            if(isWhitespace(c)) {
                lastWhitespace = true;
            } else {
                if(lastWhitespace) {
                    sp++;
                }
                if(start == -1) {
                    start = i;
                }
                end = i;
                lastWhitespace = false;
            }
        }
        if(start == -1) {
            return new String[0];
        }
        String[] res = new String[sp];
        int last = start;
        int x = 0;
        lastWhitespace = true;
        for(int i=start;i<=end;i++) {
            char c = s.charAt(i);
            boolean w = isWhitespace(c);
            if(w && !lastWhitespace) {
                res[x++] = s.substring(last,i);
            } else if(!w && lastWhitespace) {
                last = i;
            }
            lastWhitespace = w;
        }
        res[x] = s.substring(last,end+1);
        return res;
    }

    private boolean isWhitespace(char c) {
        return c==' ' || c=='\t';
    }

    private static void out(Object x) {
        System.out.println(x);
    }

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