Matt loves letter L.
A point set P is (a, b)-L if and only if there exists x, y satisfying:
P = {(x, y), (x + 1, y), . . . , (x + a, y), (x, y + 1), . . . , (x, y + b)}(a, b ≥ 1) A point set Q is good if and only if Q is an (a, b)-L set and gcd(a, b) = 1.
Matt is given a point set S. Please help him find the number of ordered pairs of sets (A, B) such that:
The first line contains only one integer T , which indicates the number of test cases.
For each test case, the first line contains an integer N (0 ≤ N ≤ 40000), indicating the size of the point set S.
Each of the following N lines contains two integers x
i, y
i, indicating the i-th point in S (1 ≤ x
i, y
i ≤ 200). It’s guaranteed that all (x
i, y
i) would be distinct.
For each test case, output a single line “Case #x: y”, where x is the case number (starting from 1) and y is the number of pairs.