B. XOR-pyramidtime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputFor an array b of length m we define the function f as   f(b) = \begin{cases} b[1] & \quad \text{if } m = 1 \\ f(b[1] \oplus b[2],b[2] \oplus b[3],\dots,b[m-1] \oplus b[m]) & \quad \text{otherwise,} \end{cases}  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)=15You 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.InputThe 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).OutputPrint q lines — the answers for the queries.ExamplesInput38 4 122 31 2Output512Input61 2 4 8 16 3241 62 53 41 2Output6030123NoteIn 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].
Input38 4 122 31 2
Output512
['dp', '*1800']