PaiGuDragon participated in a target training and shot n shots in total. The

th shot hit the points
)
in the Cartesian coordinate system, (

are integers).
The evaluation methods of training results are as follows:
Given strictly monotonically increasing sequences

and strictly monotonically decreasing sequences
The bull's-eye coordinates are
)
, where

are also integers.
For the position
)
in the

th shot, find the Manhattan distance between
)
and
* If PaiGuDragon miss the target, i.e.

,

points will be deducted
* Otherwise,

from inside to outside, that is, find the smallest

such that

, and then get

points.
The PaiGuDragon was very disappointed with his result, so he decided to redefine the position of the bull's-eye and seek the maximum score.
Please help him calculate the maximum scores he can get after redefine the position of the bull's-eye.
The first line contains 3 integers
)
.
The second line contains k integers

- Manhattan distance to bull's-eye
The third line contains k integers

- scores ordered by distance to bull's eye.

For each in next

lines contains 2 integers

- the position of the i th shot.
)