Sinkhole

There is a sinkhole at the center. To measure its depth, a stone is dropped from above the hole.

The stone starts at one edge above the hole and moves toward the opposite wall with initial horizontal speed $V$. Its initial vertical velocity is $0$. There is no air resistance and gravity is $g = 10\ \mathrm{m/s^2}$. Hence after its vertical velocity is reset to $0$, the distance it free-falls in time $t$ is $s = \frac{1}{2}gt^2 = 5t^2$ where $s$ is in $\mathrm{m}$ and $t$ is in $\mathrm{s}$.

The hole has width $W$. Whenever the stone hits a side wall, its vertical velocity becomes $0$ so the fall restarts, and its horizontal speed keeps only $80\%$ of its pre-impact magnitude while its direction reverses. Apart from the instant of impact, the horizontal speed stays constant. The stone is small enough to treat as a point.

Given the true depth $D$ of the hole, compute how many times the stone hits a wall before it reaches depth $D$.

The first line contains three integers $V$, $W$ and $D$ separated by spaces. $V$ is the initial horizontal speed in $\mathrm{m/s}$, $W$ is the width of the hole in $\mathrm{m}$, and $D$ is the true depth of the hole in $\mathrm{m}$.

Constraints:

• $V$ is an integer with $1 \le V \le 1{,}000{,}000{,}000$.
• $W$ is an integer with $1 \le W \le 1{,}000{,}000{,}000$.
• $D$ is an integer with $1 \le D \le 1{,}000{,}000{,}000$.

Print the number of times the stone hits a side wall, on one line.

The horizontal speed is constant except at the instant it hits a wall. Inputs where the stone would reach the bottom at exactly the same moment as a wall impact are not given, so simultaneous impacts with the floor and a wall do not need to be handled.