#P1528B. Kavi on Pairing Duty

Kavi on Pairing Duty

Description

Kavi has 2n2n points lying on the OXOX axis, ii-th of which is located at x=ix = i.

Kavi considers all ways to split these 2n2n points into nn pairs. Among those, he is interested in good pairings, which are defined as follows:

Consider nn segments with ends at the points in correspondent pairs. The pairing is called good, if for every 22 different segments AA and BB among those, at least one of the following holds:

  • One of the segments AA and BB lies completely inside the other.
  • AA and BB have the same length.

Consider the following example:

AA is a good pairing since the red segment lies completely inside the blue segment.

BB is a good pairing since the red and the blue segment have the same length.

CC is not a good pairing since none of the red or blue segments lies inside the other, neither do they have the same size.

Kavi is interested in the number of good pairings, so he wants you to find it for him. As the result can be large, find this number modulo 998244353998244353.

Two pairings are called different, if some two points are in one pair in some pairing and in different pairs in another.

The single line of the input contains a single integer nn (1n106)(1\le n \le 10^6).

Print the number of good pairings modulo 998244353998244353.

Input

The single line of the input contains a single integer nn (1n106)(1\le n \le 10^6).

Output

Print the number of good pairings modulo 998244353998244353.

Sample Input 1

1

Sample Output 1

1

Sample Input 2

2

Sample Output 2

3

Sample Input 3

3

Sample Output 3

6

Sample Input 4

100

Sample Output 4

688750769

Note

The good pairings for the second example are:

In the third example, the good pairings are: