For a positive integer number N, find all positive integer numbers X (if any such number exists) with the property that the number 123...X has exactly N decimal digits. Assume that N is at most 150,000.

입력 형식

The standard input has a single line which contains a positive integer number denoting the number N.

출력 형식

Your program should write the output into standard output. The first line should contain the string "NO", if such a number does not exist. Otherwise, the first line should contain a positive integer denoting how many X numbers exist. The next line (until the end of the file) should contain all X numbers found, one number per line.

예제 입력

5

예제 출력

1
8