Problem Statement

Given are sequences of $N$ integers each: $(A_1,A_2,\cdots,A_N)$ and $(B_1,B_2,\cdots,B_N)$.

Find $\sum_{1 \leq i < j \leq N} \min(A_i \oplus A_j, B_i \oplus B_j)$, where $\oplus$ denotes the bitwise XOR.

Constraints

• $1 \leq N \leq 250000$
• $0 \leq A_i,B_i < 2^{18}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N
B_1 B_2 \cdots B_N

Output

Print the answer.