Order of various functions I am to arrange the following 30 functions in terms of increasing order
( all the lg (log) are to the base 2.log* represents iterated logarithm.)

Here's my answer (the functions on the same level are of the same order):
1 ,   
lglg*n
lg*n,      lg*(lgn)








 , 
 , 
 , 

, 








I am not sure where to insert (logn)!. I know (logn)! = o((logn)^logn) and logn = o((logn)!), isn't it. But where exactly would it fit. Can anyone help me with that. Also I would really appreciate if someone could verify that my arrangement is right or not.
Thank you.
EDIT : I MEANT TO ASK THE POINT OF INSERTION OF (LOGN)! IN THE ABOVE LIST SORTED IN TERMS OF INCREASING ORDER. Simple.
Stirling's formula asserts that
$$
n! = \Theta(\sqrt{n}(n/e)^n).
$$
Thus
$$
(\log n)! = \Theta(\sqrt{\log n}((\log n)/e)^{\log n}).
$$