Problem Statement

There are length-$N$ sequences $A=(A_0,A_1,\\ldots,A_{N-1})$ and $B=(B_0,B_1,\\ldots,B_{N-1})$.
Takahashi may perform the following operation on $A$ any number of times (possibly zero):

• apply a left cyclic shift to the sequence $A$. In other words, replace $A$ with $A'$ defined by A'_i=A_{(i+1)\\% N}, where $x\\% N$ denotes the remainder when $x$ is divided by $N$.

Takahashi's objective is to maximize $\\displaystyle\\sum_{i=0}^{N-1} (A_i|B_i)$, where $x|y$ denotes the bitwise logical sum (bitwise OR) of $x$ and $y$.

Find the maximum possible $\\displaystyle\\sum_{i=0}^{N-1} (A_i|B_i)$.

What is the bitwise logical sum (bitwise OR)? The logical sum (or the OR operation) is an operation on two one-bit integers ($0$ or $1$) defined by the table below.
The bitwise logical sum (bitwise OR) is an operation of applying the logical sum bitwise.

$x$

$y$

$x|y$

$0$

$0$

$0$

$0$

$1$

$1$

$1$

$0$

$1$

$1$

$1$

$1$

The logical sum yields $1$ if at least one of the bits $x$ and $y$ is $1$. Conversely, it yields $0$ only if both of them are $0$.

Example

0110 | 0101 = 0111```

### Constraints

*   $2 \\leq N \\leq 5\\times 10^5$
*   $0\\leq A_i,B_i \\leq 31$
*   All values in the input are integers.

* * *

### Input

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

$N$
$A_0$ $A_1$ $\\ldots$ $A_{N-1}$
$B_0$ $B_1$ $\\ldots$ $B_{N-1}$

### Output

Print the maximum possible $\\displaystyle\\sum_{i=0}^{N-1} (A_i|B_i)$.

* * *

### Sample Input 1

```plain
3
0 1 3
0 2 3

Sample Output 1

8

If Takahashi does not perform the operation, $A$ remains $(0,1,3)$, and we have $\\displaystyle\\sum_{i=0}^{N-1} (A_i|B_i)=(0|0)+(1|2)+(3|3)=0+3+3=6$;
if he performs the operation once, making $A=(1,3,0)$, we have $\\displaystyle\\sum_{i=0}^{N-1} (A_i|B_i)=(1|0)+(3|2)+(0|3)=1+3+3=7$; and
if he performs the operation twice, making $A=(3,0,1)$, we have $\\displaystyle\\sum_{i=0}^{N-1} (A_i|B_i)=(3|0)+(0|2)+(1|3)=3+2+3=8$.
If he performs the operation three or more times, $A$ becomes one of the sequences above, so the maximum possible $\\displaystyle\\sum_{i=0}^{N-1} (A_i|B_i)$ is $8$, which should be printed.

Sample Input 2

5
1 6 1 4 3
0 6 4 0 1

Sample Output 2

23

The value is maximized if he performs the operation three times, making $A=(4,3,1,6,1)$,
where $\\displaystyle\\sum_{i=0}^{N-1} (A_i|B_i)=(4|0)+(3|6)+(1|4)+(6|0)+(1|1)=4+7+5+6+1=23$.