It is the apple harvest season. Alice and Bob are all set to pluck them from their farm. However, due to a certain incident, the apples are now falling down one after another. The farm in an infinite large 2D plane.

Given the initial coordinates of Alice $$$(A_x,A_y)$$$ and initial coordinates of Bob $$$(B_x,B_y)$$$ and also the coordinates where N apples will fall, you need to calculate the minimum Manhattan distance covered in total by Alice and Bob together in order to catch all apples.

• Manhattan distance between 2 coordinates $$$X_1,Y_1$$$ and $$$X_2,Y_2$$$ $$$=|X_1-X_2|+|Y_1-Y_2|$$$.
• It can be assumed that they can reach all distances without letting any apple fall down to the ground.
• Also, you need to help them catch the apples in the sequence they fall. i.e For example They can't catch the second falling apple before the first. In particular, it is necessary that all apples before the $$$i^{th}$$$ falling apple must be caught before catching the $$$i^{th}$$$ apple for all $$$1\le i \le N$$$