• 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