Inversions After Shuffle
You are given a permutation of integers from 1 to *n*. Exactly once you apply the following operation to this permutation: pick a random segment and shuffle its elements. Formally:
 1.  Pick a random segment (continuous subsequence) from *l* to *r*. All  segments are equiprobable. 1.  Let *k*<==<=*r*<=-<=*l*<=+<=1, i.e. the length of the chosen segment. Pick a random permutation of integers from 1 to *k*, *p*1,<=*p*2,<=...,<=*p**k*. All *k*! permutation are equiprobable. 1.  This permutation is applied to elements of the chosen segment, i.e. permutation *a*1,<=*a*2,<=...,<=*a**l*<=-<=1,<=*a**l*,<=*a**l*<=+<=1,<=...,<=*a**r*<=-<=1,<=*a**r*,<=*a**r*<=+<=1,<=...,<=*a**n* is transformed to *a*1,<=*a*2,<=...,<=*a**l*<=-<=1,<=*a**l*<=-<=1<=+<=*p*1,<=*a**l*<=-<=1<=+<=*p*2,<=...,<=*a**l*<=-<=1<=+<=*p**k*<=-<=1,<=*a**l*<=-<=1<=+<=*p**k*,<=*a**r*<=+<=1,<=...,<=*a**n*. 
Inversion if a pair of elements (not necessary neighbouring) with the wrong relative order. In other words, the number of inversion is equal to the number of pairs (*i*,<=*j*) such that *i*<=&lt;<=*j* and *a**i*<=&gt;<=*a**j*. Find the expected number of inversions after we apply exactly one operation mentioned above.
The first line contains a single integer *n* (1<=≤<=*n*<=≤<=100<=000) — the length of the permutation.

The second line contains *n* distinct integers from 1 to *n* — elements of the permutation.
Print one real value — the expected number of inversions. Your answer will be considered correct if its absolute or relative error does not exceed 10<=-<=9. 

Namely: let's assume that your answer is *a*, and the answer of the jury is *b*. The checker program will consider your answer correct, if .
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