Two triangles are congruent if they have the same shape and size. In other words, they are congruent if, and only if, one can be transformed into the other by a combination of translations, rotations and reflections.

The input file DATA3.txt will contain 5 lines, each line having 4 integers, separated by a single space, 0 <= A B X Y <= 8, where (A,B) specifies the bottom left corner of a rectangle, and (X,Y) specifies the top right corner of a rectangle in the cartesian plane.

The output file OUT3.txt will contain 5 lines. Each line contains the number of different (not congruent) triangles contained in the rectangle. Only consider triangles with integer coordinates inside the grid specified by (A,B) and (X,Y).

 
0 0 3 5
2 3 8 6
		        

 
108
160