201273: [AtCoder]ARC127 D - Sum of Min of Xor

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.

Sample Input 1

3
1 2 3
4 5 6

Sample Output 1

4

• $\min(1 \oplus 2, 4 \oplus 5)=\min(3,1)=1$
• $\min(1 \oplus 3, 4 \oplus 6)=\min(2,2)=2$
• $\min(2 \oplus 3, 5 \oplus 6)=\min(1,3)=1$

Thus, the answer is $1+2+1=4$.

Sample Input 2

4
1 2 3 4
1 2 3 4

Sample Output 2

24

Sample Input 3

10
195247 210567 149398 9678 23694 46151 187762 17915 176476 249828
68649 128425 249346 62366 194119 117620 26327 161384 207 57656

Sample Output 3

4019496