Problem Statement

Given is an integer sequence of length N+1: $X_0,X_1,\ldots,X_N$, where $0=X_0 < X_1 < \ldots < X_N$ holds.
Now, N people numbered 1 through N will appear on a number line.
Person i will appear at a real coordinate chosen uniformly at random from the interval [X_{i-1},X_i].
Find the expected value of the smallest distance between two people, modulo 998244353.
Definition of the expected value modulo 998244353

We can prove that the expected value in question is always a rational number.
We can also prove that, under the constraints of this problem, if we express the expected value as an irreducible fraction $\frac{P}{Q}$, we have $Q \neq 0 \pmod{998244353}$.
Thus, there uniquely exists an integer R such that $R \times Q \equiv P \pmod{998244353}, 0 \leq R < 998244353$.
Report this R.

Input

Input is given from Standard Input in the following format:
N
$X_0 X_1 \ldots X_N$

Output

Print the expected value of the smallest distance between two people, modulo 998244353.

Constraints

• $2 \leq N \leq 20$
• $0=X_0 < X_1 < \cdots < X_N \leq 10^6$

Sample Input 1

2
0 1 3

Sample Output 1

499122178

There are just two people, so the expected value of the smallest distance between two people is just the expected value of the distance between Person 1 and Person 2.
The answer is 3/2.

Sample Input 2

5
0 3 4 8 9 14

Sample Output 2

324469854

The answer is 196249/172800.

Sample Input 3

20
0 38927 83112 125409 165053 204085 246405 285073 325658 364254 406395 446145 485206 525532 563762 605769 644863 683453 722061 760345 798556

Sample Output 3

29493181

见题面 Input 部分

见题面 Output 部分