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.

Input

The input is given from Standard Input in the following format:
N
$A_1 A_2 \ldots A_{2N}$

Output

Print the answer.

Constraints

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

Sample Input 1

4
4 0 0 11 2 7 9 5

Sample Output 1

14

By rearranging A as (5, 0, 9, 7, 11, 4, 0, 2), we get $(A_1 \oplus A_2, A_3 \oplus A_4, A_5 \oplus A_6, A_7 \oplus A_8) = (5, 14, 15, 2)$, and the median of this sequence is 14.
It is impossible to rearrange A so that the median of $(A_1 \oplus A_2, A_3 \oplus A_4, A_5 \oplus A_6, A_7 \oplus A_8)$ is 15 or greater, so we print 14.

Sample Input 2

1
998244353 1000000007

Sample Output 2

1755654

Sample Input 3

5
1 2 4 8 16 32 64 128 256 512

Sample Output 3

192

见题面 Input 部分

见题面 Output 部分