Numbers
You're working with large numbers, and you want to calculate the totient function of a certain one. The totient function of a number $n$ is defined as the number of positive integers less than or equal $n$ that are relatively prime with $n$, i.e. the number of integers $k$ such that $k$ <= $n$ and $g c d (k, n) = 1$.
For example, the totient of $15$ is $8$, because 1, 2, 4, 7, 8, 11, 13, and 14 are relatively prime with $15$, while 3, 5, 6, 9, 10, 12, and 15 are not. 4 is relatively prime with 15, because there aren't any common factors of 4 and 15. 4 has factors {2}, and 15 has factors {3, 5}. On the other hand, 10 is not relatively prime with 15, because 10 and 15 both have a common factor of 5.
Given an integer $n$, figure out the value of $φ (n)$, where $φ$ represents the totient function as described above.
The only line of input contains a single positive integer $n$ less than 1000.
Output a single positive integer $p$: the value of $φ (n)$ as described above.
## Input
The only line of input contains a single positive integer $n$ less than 1000.
## Output
Output a single positive integer $p$: the value of $φ (n)$ as described above.
[samples]
**Definitions**
Let $ n \in \mathbb{Z}^+ $ with $ n < 1000 $.
Let $ \varphi(n) $ denote Euler’s totient function: the count of integers $ k \in \{1, 2, \dots, n\} $ such that $ \gcd(k, n) = 1 $.
**Constraints**
$ 1 \leq n < 1000 $
**Objective**
Compute:
$$
\varphi(n) = \left| \left\{ k \in \mathbb{Z} \mid 1 \leq k \leq n \text{ and } \gcd(k, n) = 1 \right\} \right|
$$