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 $R$.

Constraints

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

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 $998244353$.

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