Black and Red balls in a box

One day, Fidel find a large box, with some red balls and black balls in it. He know that the total number of the balls is less than 1000. Fidel wants to take exactly two balls randomly. The probability that he will take exactly two red balls is \(p\) and the probability that he will take exactly two black balls is \(q\). Fidel notices that \( p- q = \dfrac{23}{37} \). Fidel wants to find the largest possible difference between the number of red balls and the number of the black balls. Can you help Fidel by finding it?


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