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

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 — $[1,2]$.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '#!/usr/bin/env python3\n#\n# XOR-pyramid\n#\nimport sys, os\n\ndef read_int(): return int(input())\ndef read_ints(): return list(map(int, input().split()))\n#------------------------------------------------------------------------------#\n\nn = read_int()\na = read_ints()\ndp = [[0] * n for _ in range(n)]\nf = [[0] * n for _ in range(n)]\nfor i in range(n - 1, -1, -1):\n\tf[i][i] = dp[i][i] = a[i]\n\tfor j in range(i + 1, n):\n\t\tf[i][j] = f[i][j - 1] ^ f[i + 1][j]\n\t\tdp[i][j] = max(f[i][j], dp[i][j - 1], dp[i + 1][j])\nq = read_int()\nfor _ in range(q):\n\tl, r = read_ints()\n\tprint(dp[l - 1][r - 1])\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13905