A function f(N) is defined as:
f(1)=sod(1²), f(2) = sod(12²)
f(3) = sod(121²), f(4) = sod(1212²), .... and, so on

Derive the general formula for f(N) in terms of N.

*** sod(x) denotes the sum of the digits of base ten expansion of x.