Score : $600$ points

Problem Statement

A positive-integer sequence is said to be splendid if no two adjacent elements are equal.

Find the sum, modulo $998244353$, of the lengths of all splendid sequences whose elements have a sum of $N$.

Constraints

• $1 \le N \le 2 \times 10^5$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$N$

Output

Print the answer.

4

8

There are four splendid sequences whose sum is $4$: $(4),(1,3),(3,1),(1,2,1)$. Thus, the answer is the sum of their lengths: $1+2+2+3=8$.

$(2,2)$ and $(1,1,2)$ also have a sum of $4$ but ineligible because their $1$-st and $2$-nd elements are the same.

297

475867236

123456

771773807