Sinkhole

A stone bounces between the walls of a hole with its horizontal speed dropping to 80% on each wall hit and its vertical fall restarting; count wall hits before it reaches depth D.

Medium6MathSimulationImplementationNo attempts yetTime limit1sMemory limit512 MB

Problem

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 VV. Its initial vertical velocity is 00. There is no air resistance and gravity is g=10 m/s2g = 10\ \mathrm{m/s^2}. Hence after its vertical velocity is reset to 00, the distance it free-falls in time tt is s=12gt2=5t2s = \frac{1}{2}gt^2 = 5t^2 where ss is in m\mathrm{m} and tt is in s\mathrm{s}.

The hole has width WW. Whenever the stone hits a side wall, its vertical velocity becomes 00 so the fall restarts, and its horizontal speed keeps only 80%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 DD of the hole, compute how many times the stone hits a wall before it reaches depth DD.

Input

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

Constraints:

  • VV is an integer with 1V1,000,000,0001 \le V \le 1{,}000{,}000{,}000.
  • WW is an integer with 1W1,000,000,0001 \le W \le 1{,}000{,}000{,}000.
  • DD is an integer with 1D1,000,000,0001 \le D \le 1{,}000{,}000{,}000.

Output

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

Hint

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.