Count The Blocks

2000ms

262144K

Description:

You wrote down all integers from $$$0$$$ to $$$10^n - 1$$$, padding them with leading zeroes so their lengths are exactly $$$n$$$. For example, if $$$n = 3$$$ then you wrote out 000, 001, ..., 998, 999.

A block in an integer $$$x$$$ is a consecutive segment of equal digits that cannot be extended to the left or to the right.

For example, in the integer $$$00027734000$$$ there are three blocks of length $$$1$$$, one block of length $$$2$$$ and two blocks of length $$$3$$$.

For all integers $$$i$$$ from $$$1$$$ to $$$n$$$ count the number of blocks of length $$$i$$$ among the written down integers.

Since these integers may be too large, print them modulo $$$998244353$$$.

Input:

The only line contains one integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$).

Output:

In the only line print $$$n$$$ integers. The $$$i$$$-th integer is equal to the number of blocks of length $$$i$$$.

Since these integers may be too large, print them modulo $$$998244353$$$.

Sample Input:

Sample Output:

Sample Input:

Sample Output:

180 10

Informação

Provedor Codeforces

Código CF1327E