If composite function `f_1(f_2(f_3((f_n(x))))n` timesis an increasing function and if `r` of `f_i ' s` are decreasing function while rest are increasing, then the maximum value of `r(n-r)` is `(n^2-1)/4` , when `n` is an even number `(n^2)/4,` when `n` is an odd number `(n^2-1)/4,` when `n` is an odd number `(n^2)/4,` when `n` is an even number

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