Problem Statement

There are $2N$ integers written on a blackboard. The $i$-th integer is $A_i$.

Alice and Bob will play a game consisting of $N$ rounds. In each round, they do the following:

• First, Alice chooses an integer on the blackboard and erases it. Let $x$ be the integer erased here.
• Second, Bob chooses an integer on the blackboard and erases it. Let $y$ be the integer erased here.
• Finally, write the value $x \oplus y$ on a notebook, where $\oplus$ denotes the bitwise XOR.

In the end, all the integers on the blackboard will be erased, and the notebook will have $N$ integers written on it. The greatest integer written on the notebook will be the score of the game. Alice wants to maximize this score, while Bob wants to minimize it. Find the score of the game when both players play optimally under their objectives.

Constraints

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

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_{2N}

Output

Print the answer.