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E. Count The Blocks
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $998244353$.

Examples
Input
1

Output
10

Input
2

Output
180 10