Score : $500$ points

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.

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.

5
1 2 3 4 5

19

Here is a sequence of operations that achieves $\sum_{i=1}^N A_i = 19$.

• Initially, the sequence $A$ is $(1,2,3,4,5)$.
• An operation with $x = 1$ changes it to $(0,3,2,5,4)$.
• An operation with $x = 5$ changes it to $(5,6,7,0,1)$, where $\sum_{i=1}^N A_i = 5 + 6 + 7 + 0 + 1 = 19$.

5
10 10 10 10 10

50

Doing zero operations achieves $\sum_{i=1}^N A_i = 50$.

5
3 1 4 1 5

18