Given is an integer $N$. How many integers between $1$ and $N$ (inclusive) are unrepresentable as $a^b$, where $a$ and $b$ are integers not less than $2$?

Input is given from Standard Input in the following format:

```
$N$
```

Print the answer.

- $N$ is an integer. 
- $1 ≤ N ≤ 10^{10}$

6

4 and 8 are representable as $a^b$: we have $2^2=4$ and $2^3=8$.
On the other hand, 1, 2, 3, 5, 6, and 7 are unrepresentable as $a^b$ using integers a and b not less than 2, so the answer is 6.