To attract more people coming to the pool, the manager puts a number of swimming balls into the pool. He wants to calculate the level of water in the pool after putting $V$ ${m}^{3}$ of water and $n$ given balls into the pool. The ${i}^\textrm {th}$ ball is a homogeneous sphere (mass is distributed evenly) having a specific weight (or unit weight) ${w}_{i}$ and a radius ${r}_{i}$. The pool is a rectangle with dimensions $W \times L \times D$ (width by length by depth) given in meters. Your task is to calculate the level of water (measured in meters to the bottom of the pool) after putting $V$ ${m}^{3}$ of water and $n$ balls added to the pool. This level of water can be at most $D$.
We assume that the specific weight of water is $1.0$, there is no interaction among the $n$ balls, and Archimedesâ€™ principle is perfectly guaranteed.
Hints: the volume of a sphere having a radius $r$ can be computed using the following formula: $V = \frac{4}{3}\pi {r}^{3}$.
The input consists of several datasets. The first line of the input contains the number of datasets, which is a positive number and is not greater than $50$. The following lines describe the datasets.
Each dataset contains the following information:
The first line contains five integers $n, W, L, D, V$ $(1 \leq n \leq {10}^{3}, 2 \leq W, L \leq {10}^{3}, D \leq 5, V\leq W\cdot L\cdot D)$.
The ${i}^\textrm {th}$ line of the $n$ following lines contains two positive real numbers ${r}_{i}$ and ${w}_{i}$ indicating the specific weight and radius of the ${i}^\textrm {th}$ ball $(0 < {w}_{i}, {r}_{i} \leq 2)$. The real values have at most two digits after the decimal point.
For each dataset, output the water level, which should be at most $D$. Your answer is accepted iff it is correct within an absolute or relative error of ${10}^{-4}$.
Sample Input 1 | Sample Output 1 |
---|---|
2 1 2 2 2 5 1.0 1.0 1 2 2 2 5 0.8 1.0 |
2.00000000000 1.78616514621 |