Problem Statement

You are given a sequence of length $2N$: $A = (A_1, A_2, \ldots, A_{2N})$.

Find the maximum value that can be obtained as the median of the length-$N$ sequence $(A_1 \oplus A_2, A_3 \oplus A_4, \ldots, A_{2N-1} \oplus A_{2N})$ by rearranging the elements of the sequence $A$.

Here, $\oplus$ represents bitwise exclusive OR.

What is bitwise exclusive OR? The bitwise exclusive OR of non-negative integers $A$ and $B$, denoted as $A \oplus B$, is defined as follows: The number at the $2^k$ position ($k \geq 0$) in the binary representation of $A \oplus B$ is $1$ if and only if exactly one of the numbers at the $2^k$ position in the binary representation of $A$ and $B$ is $1$, and it is $0$ otherwise. For example, $3 \oplus 5 = 6$ (in binary notation: $011 \oplus 101 = 110$).

Also, for a sequence $B$ of length $L$, the median of $B$ is the value at the $\lfloor \frac{L}{2} \rfloor + 1$-th position of the sequence $B'$ obtained by sorting $B$ in ascending order.

Constraints

• $1 \leq N \leq 10^5$
• $0 \leq A_i < 2^{30}$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 \ldots A_{2N}

Output

Print the answer.