Score : $625$ points

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.

4
4 0 0 11 2 7 9 5

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 $14$.

1
998244353 1000000007

1755654

5
1 2 4 8 16 32 64 128 256 512

192