Mavis at School

Time limit3sMemory limit1024 MB

Summary

Given an array, find the segment whose maximum times its XOR sum is largest, and print that product.

Level: Hard8 of 10
Topics: Divide and conquer, Stack, Prefix sum, Trie
Solved: No attempts yet

Problem

Once upon a time, Mavis studied at a vampire school. In computer science lessons, Mavis solved problems on various topics. One of her favorite topics is arrays.

Today is the array test at the vampire school. Mavis gets this problem: given an array $a_i$ , find a segment $[l..r]$ that maximizes $max(l..r) \times xor(l..r)$ .

$max(l..r)$ is the largest number in the segment $[l..r]$ , and $xor(l..r)$ is the $\oplus$ sum of the numbers in that segment.

Help Mavis solve this problem, because she really does not want to disappoint Dracula.

Input

The first line contains a natural number $n$ ( $1 \le n \le 10^5$ ). The next line contains $n$ numbers $a_i$ ( $1 \le a_i \le 10^6$ ), the array Mavis has.

Output

Print one integer on the first line: the largest value of $max(l..r) \times xor(l..r)$ that can be found in the array.

Hint

In the first sample, the answer is the segment $[2..4]$ .

In the second sample, the answer is the segment $[5..6]$ .

Examples2

Example 1
Input
```
4
1 2 10 7
```
Expected output
```
150
```
Example 2
Input
```
6
2 3 5 3 6 8
```
Expected output
```
112
```