• محدودیت زمان: ۱ ثانیه
• محدودیت حافظه: ۲۵۶ مگابایت

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The symbol $\oplus$ represents the bitwise XOR operator for integers. For example: $$9 \oplus 3 = 1001_2 \oplus 11_2 = 1010_2 = 10$$

The \textit{value} of an array such as $a_1, a_2, \dots, a_n$ is defined as: $$a_1 \oplus a_2 \oplus \dots \oplus a_n$$

You are given two arrays of numbers, $a_1, a_2, \dots, a_n$ and $b_1, b_2, \dots, b_n$.

For each $i$ from $1$ to $n$, you can swap the values of $a_i$ and $b_i$. Write a program to perform these swaps in such a way that the sum of the values of both arrays is maximized.

ورودی

The first line of input contains a positive integer $n$, representing the length of the arrays.

$$1 \leq n \leq 10^5$$

The second and third lines each contain $n$ positive integers separated by space, with the second line representing the elements of array $a$ and the third line representing the elements of array $b$.

$$0 \leq a_i, b_i \leq 10^{18}$$

خروجی

Print a single integer, the maximum possible value for the sum of the values of both arrays.

مثال‌ها

ورودی نمونه ۱

3
1 2 3
3 1 2

خروجی نمونه ۱

6