Let S be the set which contains all poss...

Let `S` be the set which contains all possible values of `l ,m ,n ,p ,q ,r` for which `A=[[l^2-3,p,0],[0,m^2-8,q],[r,0,n^2-15]]` be non-singular idempotent matrix. Then the sum of all the elements of the set `S` is ________.

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