Find the total number of triples of integers (x, y, n) satisfying the equation \frac{1}{x}+\frac{1}{y}=\frac{1}{n^{2}}, where n is either 2012 or 2013.
Find the total number of triples of integers (x, y, n) satisfying the equation \frac{1}{x}+\frac{1}{y}=\frac{1}{n^{2}}, where n is either 2012 or 2013.