Hard Question

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Points: 5
Time limit: 1.0s
Memory limit: 16M

Problem type

A stone is dropped into a well. t seconds later, a splash is heard. The acceleration due to gravity is g metres per second per second, and the speed of sound is c metres per second. Calculate the depth of the well and the downwards velocity with which the stone hits the water.

Input Specification

Line 1: The value of g (0 < g \le 1\,000)
Line 2: The value of c (0 < c \le 1\,000)
Line 3: The value of t (0 < t \le 1\,000)

Output Specification

Line 1: The depth of the well in metres.
Line 2: The speed of the stone as it hits the water, in metres per second.

Sample Input


Sample Output


Your answers must have a relative or absolute error of less than 0.01.


The following equations may be useful:

\displaystyle \begin{align*}
\Delta \vec d &= \vec v \Delta t \\
\vec v_2 - \vec v_1 &= \vec a \Delta t \\
\Delta \vec d &= \frac 1 2 (\vec v_1 + \vec v_2) \Delta t \\
\Delta \vec d &= \vec v_1 \Delta t + \frac 1 2 \vec a (\Delta t)^2 \\
\Delta \vec d &= \vec v_2 \Delta t - \frac 1 2 \vec a (\Delta t)^2 \\
\|\vec v_2\|^2 - \|\vec v_1\|^2 &= 2 \vec a \cdot \Delta \vec d

Here \Delta t, \Delta \vec d, \vec v, \vec v_1, \vec v_2, \vec a represent time, displacement, velocity, initial velocity, final velocity, and acceleration, respectively.


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