Cool Numbers

Time limit1sMemory limit128 MB

Summary

Count integers in [a, b] that are both a perfect square and a perfect cube, meaning perfect sixth powers.

Level: Easy3 of 10
Topics: Math, Number theory, Brute force
Solved: No attempts yet

Problem

Eric likes interesting numbers such as 64. It turns out that 64 is both a perfect square and a perfect cube, since $64 = 8^2$ and $64 = 4^3$ . Eric calls such numbers cool.

Write a program that counts how many integers in a given range are cool.

Input

The first line contains an integer $a$ with $1 \le a \le 10^8$ .

The second line contains an integer $b$ with $a \le b \le 10^8$ .

Output

Print the number of cool numbers in the inclusive range from $a$ to $b$ (both $a$ and $b$ are counted if they are cool).

Examples2

Example 1
Input
```
1
100
```
Expected output
```
2
```
Example 2
Input
```
100
1000
```
Expected output
```
1
```