P5991 [PA 2015] Równanie

For a positive integer $n$, define $\operatorname{f}(n)$ as the sum of the squares of its decimal digits. Now you are given three positive integers $k, a, b$. Find the number of integers $n$ such that $a \le n \le b$ and $k \times \operatorname{f}(n) = n$.

The first line contains three positive integers $k, a, b$.

Output one integer, the number of integers $n$ that satisfy the condition.

For $100\%$ of the testdata, $1 \le k, a, b \le 10^{18}$, and $a \le b$. --- ### Sample Explanation: The $3$ valid values of $n$ are $7293$, $7854$, and $7905$. Translated by ChatGPT 5