Divide

Who doesn’t love math 🙂

Let $p$, $q$ and $n$ be natural numbers. We will say that a pair of natural numbers $(a, b)$ is interesting when:

1. $1 ≤ a ≤ p$
2. $1 ≤ b ≤ q$
3. $c = \frac{a \times b}{a + b}$ is a natural number, and $1 ≤ c ≤ n$, that is the product $a \times b$ is divisible without remainder by the sum $a + b$, and their quotient is less than or equal to $n$.

The goal of this task is simple - find the number of interesting pairs!

Write a program divide, that given the three numbers $p$, $q$ and $n$, computes the number of interesting pairs.

The only line of the standard input contains the numbers $p$, $q$ and $n$.

On the single line of the standard output, print the number of interesting pairs. It is guaranteed that the answer less than $10^{18}$.

• $1 ≤ p, q, n ≤ 10^{10}$