Problem Statement

There is an $N\times N$ grid, and Alice and Bob each keep one monster in every cell. The power of Alice's monster in cell $(i,j)$ is $A_{i,j}$, which equals $|a_i-a_j|$, and the power of Bob's monster is $B_{i,j}$, which equals $|b_i-b_j|$.

A battle took place in each of the $N^2$ cells, and the result of the battle in cell $(i,j)$ was as follows.

• If $A_{i,j}\gt B_{i,j}$, Bob's monster in cell $(i,j)$ disappears.
• If $A_{i,j}= B_{i,j}$, both Alice's and Bob's monsters in cell $(i,j)$ disappear.
• If $A_{i,j}\lt B_{i,j}$, Alice's monster in cell $(i,j)$ disappears.

Input

$N$
$a_1$ $a_2$ $\ldots$ $a_N$
$b_1$ $b_2$ $\ldots$ $b_N$

• $2\leq N\leq 2\times 10^5$
• $1\leq a_i,b_i\leq 10^9$
• All inputs are integers.

Output

Output the sum of the powers of Alice's remaining monsters and the sum of the powers of Bob's remaining monsters after the battles, in this order, each modulo $10^9+7$.

Sample

3
1 4 5
2 5 3

8 4

0 3 4    0 3 1
3 0 1    3 0 2
4 1 0    1 2 0

- - 4    - - -
- - -    - - 2
4 - -    - 2 -

4
1 2 3 4
5 6 7 8

0 0

5
700000000 200000000 800000000 600000000 100000000
700000000 800000000 100000000 300000000 900000000

199999986 199999951