Score : 600 points
We have three stones at points (0,0), (1,0), and (0,1) on a two-dimensional plane.
These three stones are said to form an L when they satisfy the following conditions:
Particularly, the initial arrangement of the stone - (0,0), (1,0), and (0,1) - forms an L.
You can do the following operation any number of times: choose one of the stones and move it to any position. However, after each operation, the stones must form an L. You want to do as few operations as possible to put stones at points (ax,ay), (bx,by), and (cx,cy). How many operations do you need to do this?
It is guaranteed that the desired arrangement of stones - (ax,ay), (bx,by), and (cx,cy) - forms an L. Under this condition, it is always possible to achieve the objective with a finite number of operations.
You will be given T cases of this problem. Solve each of them.
We assume that the three stones are indistinguishable. For example, the stone that is initially at point (0,0) may be at any of the points (ax,ay), (bx,by), and (cx,cy) in the end.
Input is given from Standard Input in the following format:
T case1 ⋮ caseT
Each case is in the following format:
ax ay bx by cx cy
Print T values. The i-th value should be the minimum number of operations for casei.
1 3 2 2 2 2 1
4
Let us use #
to represent a stone.
You can move the stones to the specified positions with four operations, as follows:
.... .... .... ..#. ..## #... -> ##.. -> .##. -> .##. -> ..#. ##.. .#.. .#.. .... ....
10 0 0 1 0 0 1 1 0 0 1 1 1 2 -1 1 -1 1 0 1 -2 2 -1 1 -1 -1 2 0 2 -1 3 -1 -2 -2 -2 -2 -3 -2 4 -3 3 -2 3 3 1 4 2 4 1 -4 2 -4 3 -3 3 5 4 5 3 4 4
0 1 2 3 4 5 6 7 8 9