Score : $1200$ points

Problem Statement

Given a positive integer $N$, find the number, modulo $998244353$, of subsets $S$ of $\{1, 2, \ldots, N\}$ that satisfy the following condition.

• Every positive integer at most $N$ can be represented as the sum of some distinct elements of $S$, and there are at most two such representations.

Constraints

• $1 \leq N \leq 1500$

Input

Input is given from Standard Input in the following format:

$N$

Output

Print the answer.

3

2

The subsets $\{1,2\}$ and $\{1,2,3\}$ satisfy the condition.

5

5

1000

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