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2017-03-15 14:00 CET

Set #09

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2017-03-22 13:59 CET
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Problem G
Inverse Factorial

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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 $n$.

Input

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

Output

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
10888869450418352160768000000
27