Functions

Let S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Define f : S \(\to\) S as

\(f(n) = \left\{ {\matrix{ {2n} & , & {if\,n = 1,2,3,4,5} \cr {2n - 11} & , & {if\,n = 6,7,8,9,10} \cr } } \right.\).

Let g : S \(\to\) S be a function such that \(fog(n) = \left\{ {\matrix{ {n + 1} & , & {if\,n\,\,is\,odd} \cr {n - 1} & , & {if\,n\,\,is\,even} \cr } } \right.\).

Then \(g(10)g(1) + g(2) + g(3) + g(4) + g(5))\) is equal to _____________.