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 $N$.

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

```
$N$
```

Print the answer.

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

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.