Problem Description

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. $1 \le a \le p$
2. $1 \le b \le q$
3. $c = \frac{a\times b}{a+b}$ is a natural number, and $1 \le c \le n$, 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.cpp, that given the three numbers $p, q$ and $n$, computes the number of interesting pairs.

Input Format

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

Output Format

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

13 17 5

11

Hint

Constraints

$1 \le p,q,n \le 10^{10}$

Subtasks