Inverse Factorial

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Ginette

A factorial $n!$ of a positive integer $n$ is defined as the product of all positive integers smaller than or equal to $n$. For example,

\[ 21! = 1 \cdot 2 \cdot 3 \cdot \ldots \cdot 21 = 51\, 090\, 942\, 171\, 709\, 440\, 000. \]It is straightforward to calculate the factorial of a small integer, and you have probably done it many times before. In this problem, however, your task is reversed. You are given the value of $n!$ and you have to find the value of $n$.

The input contains the factorial $n!$ of a positive integer $n$. The number of digits of $n!$ is at most $10^{6}$.

Output the value of $n$.

Sample Input 1 | Sample Output 1 |
---|---|

120 |
5 |

Sample Input 2 | Sample Output 2 |
---|---|

51090942171709440000 |
21 |

Sample Input 3 | Sample Output 3 |
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10888869450418352160768000000 |
27 |