Y_UME wants to play with this program. Firstly, he randomly generates an integer n∈[1,N]n∈[1,N] in equal probability. And then he randomly generates a permutation of length nn in equal probability. Afterwards, he runs the interesting program(function calculate()) with this permutation as a parameter and then gets a returning value. Please output the expectation of this value modulo 998244353998244353.
A permutation of length nn is an array of length nn consisting of integers only ∈[1,n]∈[1,n] which are pairwise different.
An inversion pair in a permutation pp is a pair of indices (i,j)(i,j) such that i>ji>j and pi<pjpi<pj. For example, a permutation [4,1,3,2][4,1,3,2] contains 44inversions: (2,1),(3,1),(4,1),(4,3)(2,1),(3,1),(4,1),(4,3).
In mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements. Note that empty subsequence is also a subsequence of original sequence.
Refer tohttps://en.wikipedia.org/wiki/Subsequence for better understanding.