Let $N$ be the number of ordered 5-tuples $(a_{1}, a_{2}, a_{3}, a_{4}, a_{5})$ of positive integers satisfying

$\frac{1}{a_{1}}+\frac{1}{a_{2}}+\frac{1}{a_{3}}+\frac{1}{a_{4}}+\frac{1}{a_{5}}=1$

Is $N$ even or odd?

Oh and [b]HINTS ONLY[/b], please do not give full solutions. Thanks.