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Problem I
POTUS
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One of the reasons the year $2025$ is interesting is because the number $2025$ can be written as a POTUS (product of two unequal squares) in a couple of ways: as $5^2 \cdot 9^2$ and as $3^2 \cdot 15^2$. Note that we did not include $1^2 \cdot 45^2$ or $9^2 \cdot 5^2$ (among others). To avoid trivial cases and overcounting, we limit consideration to expressions of the form $a^2 \cdot b^2,$ where $a$ and $b$ are integers satisfying $1 < a < b.$
Given a positive integer, $n,$ determine how many ways $n$ can be written as a POTUS.
Input
The input consists of a positive integer, $n$ $(n \leq 2^{60}).$
Output
Output a single integer, the number of ways $n$ can be written as a POTUS.
| Sample Input 1 | Sample Output 1 |
|---|---|
2025 |
2 |
| Sample Input 2 | Sample Output 2 |
|---|---|
81 |
0 |
| Sample Input 3 | Sample Output 3 |
|---|---|
1000000 |
7 |
