Task

You walk on the road of underground tunnel. You need to find the way to the destination.

Fortunately, there is a navigation system on your cell phone that shows all the paths.

Looking at the map, you know the following things:

• There is only one road. no distributor road.

• As you can see, the shape of the road is a spiral hexagon.

• In order to adapt to the road shape, navigation map uses a special coordinate system. The x axis is horizontal and the y axis is tilted(see the image above).

• You see your current location p1 and destination location p2 on the map.

• The distance from every two adjacent points on the road is 1 unit. point(0,0) to point(-1,0) is 1, point(-1,0) to point(-1,-1) is 1, point(-1,-1) to point(0,-1) is 1, and so on..

Your task is to calculate the distance between p1 and p2. The result should be a non negative integer.

Note

• p1 and p2 both are integer arrays of two elements, such as [0,1], [-1,-2], etc.. The first element means x coordinate, and the second element means y coordinate.

• 0 <= | x coordinate,y coordinate | <= 10^6

• 7 fixed testcases

• 100 random testcases, testing for correctness of solution

• All inputs are valid.

• If my reference solution gives the wrong result in the random tests, please let me know(post an issue).

Example

For p1=[0,0], p2=[1,1], the output should be 5.

For p1=[0,0], p2=[2,2], the output should be 16.

For p1=[1,0], p2=[0,1], the output should be 2.

For p1=[-1,-1], p2=[1,1], the output should be 3.

For p1=[1,1], p2=[-1,-1], the output should be 3 too.