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,\[ 21! = 1 \cdot 2 \cdot 3 \cdot \ldots \cdot 21 = 51090942171709440000. \]

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 $n$.

-----Examples-----
Sample Input 1:
120
Sample Output 1:
5

Sample Input 2:
51090942171709440000
Sample Output 2:
21

Source: kattis | Difficulty: HARD
Tags: Mathematics


Solutions: