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## Problem Description

Given a number n, find the smallest factorial that is a multiple of n. (Eg. 4 factorial is a multiple of 12)

A *n* factorial is a product of all the whole numbers from 1 to *n*. (Eg. 4 factorial = 4 x 3 x 2 x 1)

## Input

The input consists of an single integer, the number. It is guaranteed that the number will be a strictly positive integer not exceeding 1 million.

## Output

The smallest fractorial which is a multiple of the supplied integer.

## Note

For this question, you are supposed to input from 'fractorial.in' and output to 'fractorial.out'.

## Sample Input

12

## Sample Output

4

### Tags

### Subtasks and Limits

Subtask | Score | #TC | Time | Memory | Scoring |
---|---|---|---|---|---|

1 | 20 | 10 | 1s | 64MB | Minimum |

2 | 30 | 10 | 1s | 64MB | Minimum |

3 | 50 | 10 | 1s | 64MB | Minimum |

4 | 0 | 1 | 1s | 64MB | Minimum |

### Judge Compile Command

g++-8 ans.cpp -o fractorial -Wall -Wshadow -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512