Description

Original source: CODECHEF September Challenge 2015 REBXOR

Given an array $A$ of $N$ elements, indexed starting from 1. Find the maximum value of the following expression: $(A[l_1]\bigoplus A[l_1+1]\bigoplus …\bigoplus A[r_1])+ (A[l_2]\bigoplus A[l_2+1]^…\bigoplus A[r_2])$, where $1\le l_1\le r_1<l_2\le r_2\le N$, and $x\bigoplus y$ denotes the bitwise XOR of $x$ and $y$.

Input Format

The first line of input contains an integer $N$, representing the number of elements in the array.

The second line contains $N$ integers $A[1], A[2], \ldots, A[N]$.

Output Format

Output a single line containing the maximum possible value of the given expression.

Sample 1

Valid $(l_1,r_1,l_2,r_2)$ pairs include: $(1,2,3,3),(1,2,4,5),(3,3,4,5)$.

5
1 2 3 1 2

6

Constraints and Hints

For $100\%$ of the data, $2\le N \le 4\times 10^5, 0\le A_i\le 10^9$.