Factorial Digit Count

Given a positive integer $N$, find every positive integer $X$ such that $1 \times 2 \times 3 \times \cdots \times X$ (that is, $X!$) has exactly $N$ decimal digits. Such an $X$ may not exist. You may assume $1 \le N \le 150000$.

The first line of input contains a single positive integer $N$.

If no such $X$ exists, print the string NO on the first line. Otherwise, print on the first line how many values of $X$ satisfy the condition, then print all such $X$ in increasing order, one per line.