1. [12 marks) Order all the following twelve functions by order of growth from slowest to fastest. That is, find an arrangement f(n), f2(n),... ,/i2(n) of these functions such that fi-O(f2(n), f O(fa(n)),..., fu O(f12(n)). Partition your list into groups such that two functions f(n) and g(n) are in the same group if and only if f(n) e(g(n). Vigngn,4 2 n1.001, nign, 1000n2, 000 n 1000Vn, n2 - 20n, lg n/(lg lg n), (Inn)1/2 You are NOT required to justify your ordering