Mr. Panda has recently fallen in love with a new game called Square Off, in which players compete to find as many different squares as possible on an evenly spaced rectangular grid of dots. To find a square, a player must identify four dots that form the vertices of a square. Each side of the square must have the same length, of course, but it does not matter what that length is, and the square does not necessarily need to be aligned with the axes of the grid. The player earns one point for every different square found in this way. Two squares are different if and only if their sets of four dots are different.
Mr. Panda has just been given a grid with
Input Specification
The first line of the input gives
Output Specification
For each test case, output one line containing Case #x: y
, where x
is the test case number (starting from y
is the number of different squares which can be found in the grid.
Limits
Subtask 1 [8/25]
Subtask 2 [17/25]
Sample Input
4
2 4
3 4
4 4
1000 500
Sample Output
Case #1: 3
Case #2: 10
Case #3: 20
Case #4: 624937395
Explanation
The pictures below illustrate the grids from the first three sample cases, and a valid square in the third sample case.
Comments