Problem Description

Let $e = 2.718\cdots$ be the base of the natural logarithm, and $\pi = 3.141\cdots$ be the ratio of the circumference of a circle to its diameter.

For a positive integer $ n $, define the real number $ f(n) $ as follows. Consider a circle $ C $ with center $ (0, 0) $ and radius $ 1 $ on the coordinate plane. Define points $P_0, P_1, \ldots, P_{n-1}$ on $ C $ such that the coordinates of $ P_j $ are $(\cos(2 \pi e j), \sin(2 \pi e j))$ for $j = 0, 1, \ldots, n - 1$. It can be proven that $P_0, P_1, \ldots, P_{n-1}$ are distinct, so $ C $ is divided into $ n $ arcs by these points. Let $ f(n) $ be the maximum length of these arcs.

Illustration for $ n = 10 $

It can be proven that there are infinitely many positive integers $ n $ such that $ f(n) > f(n + 1) $. Let these integers be $n_1, n_2, \ldots$ in ascending order.

Given a positive integer $ K $, it can be proven that there uniquely exist integers $ a, b $ such that $f(n_K) = 2 \pi (a + e b)$. Find the remainders of $ n_K, a, b $ when divided by $ 998244353 $ (each should be between $ 0 $ and $ 998244353 - 1 $).

Input Format

The input is given from the standard input in the following format:

$ K $

Output Format

Output the remainders of $ n_K, a, b $ when divided by $ 998244353 $ in order.

Sample Input and Output

Sample Input #1

1

Sample Output #1

1 1 0

Sample Input #2

2

Sample Output #2

2 998244351 1

Sample Input #3

5

Sample Output #3

10 998244345 3

Notes/Hints

Constraints

• $1 \le K \le 10^{11}$.

Sample Explanation 1

$ n_1 = 1 $, $f(1) = 2 \pi$.

Sample Explanation 2

$ n_2 = 2 $, $f(2) = 2 \pi (-2 + e)$.

Sample Explanation 3

$ n_5 = 10 $, $f(10) = 2 \pi (-8 + 3 e)$.

见题面 Input 部分

见题面 Output 部分