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

You must perform the following operation on each index exactly 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

Output format
Print a single integer that denotes the maximum value of \(S\).

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