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. $\displaystyle c=\frac{a \cdot b}{a + b}$ is a natural number, and 1 ≤ c ≤ n, that is the product $a \cdot b$ 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!

Task

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

Input

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

Output

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

Constraints

• $1 ≤ p, q, n ≤ 10^{10}$

Subtask 1 (5 points)

• $1 ≤ p, q, n ≤ 2 \cdot 10^4$

Subtask 2 (10 points)

• $1 ≤ p, q, n ≤ 2.5 \cdot 10^7$

Subtask 3 (10 points)

• $1 ≤ p, q, n ≤ 2.5 \cdot 10^8$

Subtask 4 (10 points)

• $1 ≤ p, q, n ≤ 2 \cdot 10^9$

Subtask 5 (10 points)

• $n = 10^{10}$
• p = q

Subtask 6 (10 points)

• $n = 10^{10}$

Subtask 7 (45 points)

• No other constraints

Examples

stdin

13 17 5

stdout

11