Arrange the following functions in their increasing order of growth. In options $\log ^{2} n$ means $(\log n)^{2}$
- $\log (n !), \log ^{2} n, (\lg n) !, e^{n}$
- $\log (n !), \log ^{2} n, e^{n}, (\lg n) !$
- $\log ^{2} n, \log (n !), (\lg n) !, e^{n}$
- $\log ^{2} n, (\lg n) !, \log (n !), e^{n}$
