If composite function `f_1(f_2(f_3((f_n(x))))n` timesis an decreasing function and if `'r'` functions out of total `'n'` functions are decreasing function while rest are increasing, then the maximum value of `r(n-r)` is (a) `(n^2-4)/4` , when `n` is of the form 4k (b) `(n^2)/4,` when `n` is an even number (c) `(n^2-1)/4,` when `n` is an odd number (d) `(n^2)/4,` when `n` is of the form 4k+2

Options

A. `(n^(2)-1)/(4)` when n is an even number
B. `n^(2)/(4)` when n is an odd number
C. `(n^(2)-1)/(4)` when n is odd number
D. None of these