For each permutation \(a_1,a_2,a_3,\cdots,a_{10}\) of the integers \(1,2,3,\cdots,10\), form the sum $$|a_1-a_2|+|a_3-a_4|+|a_5-a_6|+|a_7-a_8|+|a_9-a_{10}|$$ The average value of all such sums can be written in the form \(\frac{p}{q}\), where \(p\) and \(q\) are relatively prime positive integers. Find \(p+q\).

(第十四届AIME1996 第12题)