Problem Statement

In a certain game, a score is awarded according to the content of the play.

The score metrics consist of a provisional score and bonus points, and the sum of the provisional score and the bonus points is called the true score. Here, the provisional score, the bonus points, and the true score are all always integers between $0$ and $10^5$, inclusive.

Now, $N$ players played this game, and the bonus points of the $i$-th player were $A_i$.

In addition, the following is known about the scores of these $N$ players.

• Letting $B_i$ be the provisional score of the $i$-th player, $B_1 \leq B_2 \leq \dots \leq B_N$ holds.
• Letting $C_i$ be the true score of the $i$-th player, $C_1 \leq C_2 \leq \dots \leq C_N$ holds.

Find the total number of possible combinations of the true scores of the $N$ players, modulo $998244353$.

Note that $2$ combinations are distinguished if there exists a player whose true score differs between them.

Constraints

• All inputs are integers.
• $1 \leq N \leq 200$
• $0 \leq A_i \leq 10^5$

Input

The input is given from standard input in the following format.

$N$
$A_1$ $A_2$ $\dots$ $A_N$

Output

Output the answer.

Sample

2
1 99998

6

1
0

100001

9
31 41 59 26 53 58 97 93 23

454568508