Baltic Olympiad in Informatics: 2003 Day 1, Problem 1

Some amount of water is poured into a barrel, then a number of cubes of different size and density are put into water. Finally, a lid is put onto the barrel and pushed down until it touches the edges of the barrel.

Write a program to compute the resulting water level in the barrel.

It can be assumed that:

• the density of water is ~1.0~,
• the influence of air can be neglected,
• the cubes fit completely into the barrel,
• the cubes do not rotate and do not touch each other.

Input Specification

The first line contains three real numbers - the bottom area of the barrel ~S~ ~(0 < S \le 1\,000)~, the height of the barrel ~H~ ~(0 < H \le 1\,000)~, and the volume of the water ~V~ ~(0 < V \le S \cdot H)~. The next line contains the number of cubes ~N~ ~(0 < N \le 1\,000)~. It is followed by ~N~ lines, each containing two real numbers describing the cube - the length of a side of the cube ~L~ ~(0 < L \le 1\,000)~, and the density of the cube ~D~ ~(0 < D \le 10)~.

Output Specification

The first and only line of the output must contain one real number - the resulting water level. The output must not differ from the correct value by more than ~10^{-4}~.

Sample Input

100 10 500
1
1 0.5

Sample Output

5.0050