Maximum Xor Secondary

Source: Codeforces

Version: Phuoc Hung OJ Extended

Problem Statement

Given a sequence $s_1,s_2,\ldots,s_n$ of pairwise distinct positive integers. For every contiguous subarray of length at least two, take its largest and second largest values and compute their bitwise XOR. Find the maximum XOR over all valid subarrays.

Input

The first line contains $n$. The second line contains $n$ pairwise distinct integers $s_1,s_2,\ldots,s_n$.

Output

Print one integer: the maximum possible XOR value.

Subtasks

• Subtask 1 (30 points): $n\le2000$; all other conditions are unchanged.
• Subtask 2 (70 points): $2\le n\le10^5$, $1\le s_i\le10^9$, các $s_i$ đôi một khác nhau.

Examples

Input

5
5 2 1 4 3

Output

7

Explanation

The sequence is $[5,2,1,4,3]$. For each subarray of length at least two, take its largest and second-largest values and compute their XOR.

Some subarrays that determine the maximum are:

• $[1..2]=[5,2]$: the two largest values are $5$ and $2$, so $5\oplus2=7$.
• $[2..4]=[2,1,4]$: the two largest values are $4$ and $2$, so $4\oplus2=6$.
• $[3..4]=[1,4]$: $4\oplus1=5$.
• $[4..5]=[4,3]$: $4\oplus3=7$.
• Longer subarrays containing both $5$ and $4$ have largest values $5$ and $4$, giving $5\oplus4=1$.

No subarray produces a value greater than $7$, while $[1..2]$ and $[4..5]$ both attain $7$. Therefore the program prints 7.