We say that permutation p of size n is connected if there is no k, \(1\leqslant k < n\), such that \(p(1), p(2), \dots, p(k)\) is permutation of \(1,2,\dots, k.\)
You are given a positive integer n. Find out number of connected permutations of size \(1,2,\dots,n\). As this numbers can be large, print them modulo \(924844033.\)

Input Format:
Single line containing integer n.

Output Format:
Output n lines, numbers of connected permutations of size \(1, 2, \dots, n\).

Constraints:
\( 1 \leqslant n \leqslant 500,000.\)

50 points
\(n \leqslant 5,000.\)