You are given three arrays $A, B,\ and\ C$. All three arrays consist of $N$ integers.

You can perform the following operation on each index for at most one time:

• $Convert(i)$: Select a positive value $D$ such that $C_i\ \&\ D = D$ and update $B_i = B_i \oplus D$. Here, $\oplus$ and $\&$ denotes the bitwise XOR operation and bitwise AND operation.

You are required to maximize the following expression:

$S = \sum_{i=1}^{n} A_i \oplus B_i$    

Input format

• First line: A single integer $N$ denoting the number of elements of the array
• Next line: $N$ integers of array $A$
• Next line: $N$ integers of array $B$
• Next line: $N$ integers of array $C$

Output format
Print a single integer that denotes the maximum value of $S$.

Constraints
$1 \leq N \leq 10^5$
$1 \leq A_i, B_i, C_i < 2^{30}$