AT_abc450_g [ABC450G] Random Subtraction

You are given a sequence $ A $ of $ N $ non-negative integers. Repeat the following operation until $ A $ has exactly one element. - Choose two distinct integers $ i $ and $ j $ satisfying $ 1 \leq i, j \leq |A| $ uniformly at random. - Let $ a $ and $ b $ be $ A_i $ and $ A_j $ , respectively. - Remove the $ i $ -th and $ j $ -th elements from $ A $ . - Append $ a - b $ to the end of $ A $ . Let $ x $ be the only element of $ A $ at the end. Find the expected value of $ x^2 $ , modulo $ 998244353 $ . Definition of expected value modulo $ 998244353 $ It can be proved that the expected value to be found is always a rational number. It can also be proved that under the constraints of this problem, when expressed as an irreducible fraction $ \frac{P}{Q} $ , we have $ Q \neq 0 \pmod{998244353} $ . Thus, there is a unique integer $ R $ satisfying $ R \times Q \equiv P \pmod{998244353}, 0 \leq R < 998244353 $ . Find this $ R $ .

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

Output the answer on a single line.

### Sample Explanation 1 First, choosing $ (i, j) = (3, 1) $ makes the sequence $ (5, -4) $ . Next, choosing $ (i, j) = (1, 2) $ makes the sequence $ (9) $ . $ x^2 $ equals $ 81 $ with probability $ \frac{1}{3} $ and $ 1 $ with probability $ \frac{2}{3} $ , so the expected value is $ \frac{83}{3} $ . ### Constraints - $ 1 \leq N \leq 2 \times 10^5 $ - $ 0 \leq A_i \leq 998244352 $ - All input values are integers.