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 $998244353$.