Problem Statement

You are given a sequence of non-negative integers $A = (A_1, \ldots, A_N)$. You can do the operation below any number of times (possibly zero).

• Choose an integer $x\in \{A_1,\ldots,A_N\}$.
• Replace $A_i$ with $A_i\oplus x$ for every $i$ ($\oplus$ denotes the bitwise $\mathrm{XOR}$ operation).

Find the maximum possible value of $\sum_{i=1}^N A_i$ after your operations.

What is bitwise $\mathrm{XOR}$? The bitwise $\mathrm{XOR}$ of non-negative integers $A$ and $B$, $A \oplus B$, is defined as follows: When $A \oplus B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if exactly one of $A$ and $B$ is $1$, and $0$ otherwise. For example, we have $3 \oplus 5 = 6$ (in base two: $011 \oplus 101 = 110$).

Constraints

• $1\leq N \leq 3\times 10^{5}$
• $0\leq A_i < 2^{30}$

Input

Input is given from Standard Input from the following format:

N
A_1 \ldots A_N

Output

Print the maximum possible value of $\sum_{i=1}^N A_i$ after your operations.