Problem Statement

In competitive programming, an array of length $n$ is usually given as input on a single line, separated by spaces, like this:

$a_1\ a_2\dots a_n$

as shown above.

In this problem, the array $a$ is assumed to be input in the format above.

Here, for an array $a$, we define $f(a)=aを入力で与えた時の入力の長さ$, that is, the length of the input when the array is given as input (excluding the trailing newline).

How many arrays $a$ of length $n$ whose elements are all positive integers satisfy $f(a)=\sum_{i=1}^{n}a_i$?

Since the answer can be very large, output it modulo $998244353$.

Here, arrays $x,y$ of length $K$ are considered different if there exists at least one integer $i$ such that $x_i\ne y_i (1≤i≤K)$.

(Added on 2022/6/4)

The input length of the array $a$ means the length of $a$ viewed as a string, that is, the total of the number of digits of each element of $a$ and the number of separating spaces.

Also, each element of $a$ is given in base $10$.

Input

$n$

• The 1st line contains an integer $n$.
• $1≤n≤200$
• $n$ is an integer.

Output

Output the answer on 1 line. Do not forget to output it $\mod\ 998244353$. Print a newline at the end.

Sample

2

2

1

1

17

609415864