A Pythagorean triangle is a right triangle in which all three sides are integer lengths. Let \(a, b\) be the legs of a Pythagorean triangle, and \(h\) be the altitude to the hypotenuse.

How many non-congruent triangles are there such that \(\large \frac {1}{a} +\frac{1}{b} +\frac{1}{h}=1\).

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