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

9.80
334
3.41

Sample Output

51.90
31.90

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

Notes

The following equations may be useful:

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

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.