E. Inversions After Shuffletime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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:  Pick a random segment (continuous subsequence) from l to r. All  segments are equiprobable.  Let k = r - l + 1, i.e. the length of the chosen segment. Pick a random permutation of integers from 1 to k, p1, p2, ..., pk. All k! permutation are equiprobable.  This permutation is applied to elements of the chosen segment, i.e. permutation a1, a2, ..., al - 1, al, al + 1, ..., ar - 1, ar, ar + 1, ..., an is transformed to a1, a2, ..., al - 1, al - 1 + p1, al - 1 + p2, ..., al - 1 + pk - 1, al - 1 + pk, ar + 1, ..., an. 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 < j and ai > aj. Find the expected number of inversions after we apply exactly one operation mentioned above.InputThe 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.OutputPrint 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 .ExampleInput32 3 1Output1.916666666666666666666666666667
Input32 3 1
Output1.916666666666666666666666666667
['data structures', 'probabilities', '*2400']