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.

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