Score: $800$ points

问题陈述

给定一个由 $N$ 个非负整数组成的序列 $A=(A_1,A_2,\dots,A_N)$。考虑对这个序列执行以下操作 $N-1$ 次，以获得长度为 $1$ 的序列：

• 设 $n$ 为 $A$ 的长度。首先，你可以随意重新排列 $A$ 中的元素。然后，用一个由 $n-1$ 个非负整数组成的序列 $(A_1 \oplus A_2, A_2 \oplus A_3, \dots, A_{n-1} \oplus A_n)$ 替换 $A$。

这里，$\oplus$ 表示按位 $\mathrm{XOR}$ 操作。

设 $X$ 为在执行了 $N-1$ 次操作后得到的、长度为 $1$ 的序列中的项的值。找出 $X$ 的最大可能值。

什么是按位 $\mathrm{XOR}$ 操作？

两个非负整数 $A$ 和 $B$ 的按位 $\mathrm{XOR}$，记作 $A \oplus B$，定义如下：

• 在 $A \oplus B$ 的二进制表示中，$2^k$（$k \geq 0$）位上的数字如果是 $1$，则当且仅当在 $A$ 或 $B$ 的 $2^k$ 位上是 $1$ 但不是两者都是 $1$ 时，它就是 $1$；否则是 $0$。

例如，$3 \oplus 5 = 6$（二进制：$011 \oplus 101 = 110$）。 一般来说，$k$ 个非负整数 $p_1, p_2, p_3, \dots, p_k$ 的按位 $\mathrm{XOR}$ 定义为 $(\dots ((p_1 \oplus p_2) \oplus p_3) \oplus \dots \oplus p_k)$，并且可以证明这与 $p_1, p_2, p_3, \dots, p_k$ 的顺序无关。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

You are given a sequence of $N$ non-negative integers $A=(A_1,A_2,\dots,A_N)$. Consider performing the following operation $N-1$ times on this sequence to obtain a sequence of length $1$:

• Let $n$ be the length of $A$. First, rearrange the elements in $A$ in any order you like. Then, replace $A$ with a sequence of $n-1$ non-negative integers $(A_1 \oplus A_2, A_2 \oplus A_3, \dots, A_{n-1} \oplus A_n)$.

Here, $\oplus$ represents the bitwise $\mathrm{XOR}$ operation.

Let $X$ be the value of the term contained in the sequence of length $1$ obtained after $N-1$ operations. Find the maximum possible value of $X$.

What is the bitwise $\mathrm{XOR}$ operation?

The bitwise $\mathrm{XOR}$ of two non-negative integers $A$ and $B$, denoted as $A \oplus B$, is defined as follows:

• In the binary representation of $A \oplus B$, the digit at the $2^k$ ($k \geq 0$) position is $1$ if the digit at the $2^k$ position is $1$ in $A$ or $B$ but not both, and $0$ otherwise.

For example, $3 \oplus 5 = 6$ (in binary: $011 \oplus 101 = 110$).
In general, the bitwise $\mathrm{XOR}$ of $k$ non-negative integers $p_1, p_2, p_3, \dots, p_k$ is defined as $(\dots ((p_1 \oplus p_2) \oplus p_3) \oplus \dots \oplus p_k)$, and it can be proved that this does not depend on the order of $p_1, p_2, p_3, \dots, p_k$.

Constraints

• $2 \leq N \leq 100$
• $0 \leq A_i < 2^{60}$
• All input values are integers.

Input

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

$N$

$A_1$ $A_2$ $\dots$ $A_N$

Output

Print the answer.

Sample Input 1

4
1 2 3 4

Sample Output 1

7

The sequence $A$ can be transformed into $A=(7)$ by the following three operations:

• In the first operation, rearrange $A=(1,2,3,4)$ to $(3,1,4,2)$. $A$ is replaced with $(3 \oplus 1, 1 \oplus 4, 4 \oplus 2) = (2,5,6)$.
• In the second operation, rearrange $A=(2,5,6)$ to $(2,6,5)$. $A$ is replaced with $(2 \oplus 6, 6 \oplus 5) = (4,3)$.
• In the third operation, rearrange $A=(4,3)$ to $(4,3)$. $A$ is replaced with $(4 \oplus 3) = (7)$.

Sample Input 2

13
451745518671773958 43800508384422957 153019271028231120 577708532586013562 133532134450358663 619750463276496276 615201966367277237 943395749975730789 813856754125382728 705285621476908966 912241698686715427 951219919930656543 124032597374298654

Sample Output 2

1152905479775702586