Partition into Rectangles

Limits: 2 sec., 256 MiB

This statement was translated automatically from Ukrainian.

Marichka has points \((x, y)\) on the plane for all integers \(x, y\) such that \(0 \le x < n, 0 \le y < m\). She connected some \(k\) pairs of points with each other.

Zenyk wants to partition the entire region into rectangles such that connected points belong to different rectangles. To do this, he chooses positive integers \(a\) and \(b\) such that \(a \le n, b \le m\), and draws a horizontal line every \(a\) points and a vertical line every \(b\) points. Thus, the region will be divided into \(\left \lceil{\frac{n}{a}}\right \rceil \cdot \left \lceil{\frac{m}{b}}\right \rceil\) (division rounded up) rectangles. More formally, the point \((x, y)\) will belong to the rectangle with coordinates \(\left(\left \lfloor{\frac{x}{a}}\right \rfloor, \left \lfloor{\frac{y}{b}}\right \rfloor \right)\) (integer division).

Marichka told Zenyk that she does not like small rectangles. Therefore, Zenyk must maximize the product \(a \cdot b\).

Help Zenyk, write a program for him.

Input

The first line contains three integers \(n\), \(m\), \(k\).

The next \(k\) lines contain four integers \(x_1, y_1, x_2, y_2\). This means that the point \((x_1, y_1)\) is connected to the point \((x_2, y_2)\).

Output

In a single line, print an integer — the maximum possible product \(a \cdot b\).

Constraints

\(1 \le n, m \le 200\),

\(1 \le k \le 10^5\),

\(0 \le x < n, 0 \le y < m\) for all points encountered in the input,

\((x_1, y_1) \ne (x_2, y_2)\) for all pairs of points that are connected to each other,

each pair of connected points appears only once,

for 15 tests, additional constraints \(n, m \le 100, k \le 10^3\) hold.

Samples

Input (stdin) сopy	Output (stdout) сopy
4 7 7 0 6 1 2 1 3 2 2 3 4 2 0 3 2 1 1 0 1 0 4 0 5 3 5 3 6 1 6	9

Notes

In the example, it is optimal to choose \(a=3,b=3\).