After a tiring practical test at OOP, Rares is faced with a new challenge. He has to solve the following problem, otherwise he will fail the Programming class.

Let $v$ be an array of $n$ non-negative integers. Find the maximum value of $(v_i \oplus v_j) \times (v_k + v_l)$, where $1 \le i < j < k < l \le n$. Here $\oplus$ represents the bitwise xor operation.

Help Rares save his GPA!

Input data

The first line of the input contains $n$ ($4 \le n \le 200 \ 000$), the size of the given array.

The next line contains $n$ non-negative integers $v_1$, $v_2$, $\dots$, $v_n$ ($0 \le v_i \le 2^{30}-1$).

Output data

Output a single number, the maximum value of $(v_i \oplus v_j) \times (v_k + v_l)$, where $1 \le i < j < k < l \le n$.

Constraints and clarifications

• For $20$ points, it is guaranteed that $n \le 200$;
• For another $20$ points, it is guaranteed that $n \le 2 \ 000$;
• For the last $60$ points, we have $n \leq 200 \ 000$;

Example 1

stdin

6
12 42 2 0 145 7

stdout

6384

Explanation

Rares chooses $i=2$, $j=4$, $k=5$, $l=6$. The value is $(42 \oplus 0) \times (145 + 7) = 6384$.