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B. XOR-pyramid

time limit per test

2 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputFor an array $$$b$$$ of length $$$m$$$ we define the function $$$f$$$ as

where $$$\oplus$$$ is bitwise exclusive OR.

For example, $$$f(1,2,4,8)=f(1\oplus2,2\oplus4,4\oplus8)=f(3,6,12)=f(3\oplus6,6\oplus12)=f(5,10)=f(5\oplus10)=f(15)=15$$$

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 $$$a_l, a_{l+1}, \ldots, a_r$$$.

Input

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

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

The third line contains a single integer $$$q$$$ ($$$1 \le q \le 100\,000$$$) — the number of queries.

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

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 — $$$[1,2]$$$.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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