AT_abc468_e [ABC468E] Sum of Average

You are given a positive integer $ N $ and a length- $ N $ integer sequence $ A=(A_1,A_2,\ldots,A_N) $ . Define $ f(l,r) $ as the (arithmetic) mean of $ A_l,A_{l+1},\ldots,A_r $ . Find $ \displaystyle \sum_{1\le l\le r\le N} f(l,r) $ , modulo $ 998244353 $ . :::info[Definition of a rational number modulo $ 998244353 $] Under the constraints of this problem, it can be proved that the rational number to be found is always an irreducible fraction $ \frac{P}{Q} $ such that $ Q {{}\not\equiv{}} 0 \pmod{998244353} $ . Thus, there is a unique integer $ R $ such that $ R \times Q \equiv P \pmod{998244353}, 0 \leq R

The input is given from Standard Input in the following format: > $ N $ > $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $

Output the answer.

### Sample Explanation 1 We have $ \displaystyle f(1,1)=2,f(1,2)=\frac{2+3}2=\frac52,f(2,2)=3 $ . Thus, $ \displaystyle \sum_{1\le l\le r\le N} f(l,r)=2+\frac52+3=\frac{15}2 $ . $ \displaystyle \frac{15}2 $ in modulo- $ 998244353 $ expression is $ 499122184 $ , so output $ 499122184 $ . ### Constraints - $ 1\le N\le 5\times 10^5 $ - $ 0\le A_i < 998244353 $ - All input values are integers.