Knocker

I am the danger. A guy opens his door and gets shot, and you think that of me? No. I am the one who knocks!

• Walter White, Breaking Bad

It's well-known that Walter is the one who knocks. But did you know that he can knock with strength $x$ for every positive integer $x$?

He has an array $a_1, a_2, \ldots, a_n$ of positive integers. If he knocks with strength $x$, then, for each $1 \leq i \le n$, $a_i$ will be replaced with $a_i \bmod x$.

How many different arrays $a_1, a_2, \ldots, a_n$ can Walter achieve by knocking any number of times? As the number can be very large, output it modulo $998 \ 244 \ 353$.

Here $x \bmod y$ denotes the remainder of $x$ when dividing by $y$. For example, $6 \bmod 3 = 0$, and $6 \bmod 4 = 2$.

Input data

The first line of the input contains a single integer $n$ ($1 \leq n \leq 500$) - the length of the array.

The second line of the input contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 500$) - the elements of the array.

Output data

Output a single integer - the number of different arrays Walt can achieve by knocking.

Example 1

stdin

1
5

stdout

4

Explanation

In the first sample, you can get the following arrays: $[5], [2], [1], [0]$.

Example 2

stdin

2
6 5

stdout

7

Explanation

In the second sample, you can get the following arrays: $[6, 5], [2, 1], [1, 0], [0, 5], [0, 2], [0, 1], [0, 0]$.

Example 3

stdin

5
1 2 4 8 16

stdout

69