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)