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 $S$ $(0<S\le 1000)$, the height of the barrel $H$ $(0<H\le 1000)$, and the volume of the water $V$ $(0<V\le S\cdot H)$. The next line contains the number of cubes $N$ $(0<N\le 1000)$. It is followed by $N$ lines, each containing two real numbers describing the cube - the length of a side of the cube $L$ $(0<L\le 1000)$, 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