## BOIFAC - BOI 97 - Factorial

For a positive integer number N, find all positive integer numbers X (if any such number exists) with the property that the number 1*2*3*...*X has exactly N decimal digits. Assume that N is at most 150,000.

### Input

A single line which contains a positive integer number denoting the number N.

### 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. Then print all the X numbers, one number per line.

### Example

Input:5Output:1 8

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Hitman:
2013-05-23 20:12:32
@Mir Wasi Ahmed My score is 100 for this problem in my first attempt But i haven't got any points for this prob. Why ??? |

Added by: | Mir Wasi Ahmed |

Date: | 2008-12-31 |

Time limit: | 0.200s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | C CPP C99 JAVA PAS-GPC PAS-FPC |

Resource: | Balkan Olympiad of Informatics 1997 |