Happy Valentine's Day!

You have a mixture of red and blue hearts (made of paper, not the real one), and you want to gift some of those hearts to your favorite girl. You have 1991 in all. It so happens that when you take two hearts randomly without replacement, there is a probability of exactly \(\dfrac{1}{2}\) that both are red or both are blue. What is the largest possible number of red hearts with you that is consistent with this data ?

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