10907: ABC361 - F - x = a^b
[Creator : ]
Description
How many integers $x$ between $1$ and $N$, inclusive, can be expressed as $x = a^b$ using some positive integer $a$ and a positive integer $b$ not less than $2$?
Input
The input is given from Standard Input in the following format:
```
$N$
```
```
$N$
```
Output
Print the answer as an integer.
Constraints
- All input values are integers.
- $1 \le N \le 10^{18}$
- $1 \le N \le 10^{18}$
Sample 1 Input
99
Sample 1 Output
12
The integers that satisfy the conditions in the problem statement are $1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81$: there are $12$.
Sample 2 Input
1000000000000000000
Sample 2 Output
1001003332