Preparation

Python has a built-in function to calculate logarithms. This function, however, is in the math module, which you first need to import before you can work with the additional functionality disclosed therein. Below is a small piece of code that this module imports and calculates the logarithm with base 10 of the number 100.

>>> import math
>>> math.log(100, 10)
2.0

See page 67 and 68 in the manual for more information on the math module.

Assignment

The Palermo Technical Impact Hazard Scale is a logarithmic scale used by astronomers to rate the potential hazard of impact of a meteorite. It combines three types of data into a single "hazard" value: the number of years until the impact ($$\Delta t$$), the probability of impact ($$P_i$$), and the estimated kinetic yield ($$E_i$$), which is calculated based on the estimated size and impact speed of the meteorite.The value of the Palermo Scale ($$\mathcal P$$) is defined as a common logarithm \[ \mathcal P = \log_{10}\frac{P_i}{f_b\times\Delta_t}\,. \] In which $$\Delta_t$$ represents the number of years between now and the time of impact and $$f_b$$ is the background impact frequency of annual impacts on earth. The background impact frequency is defined for this purpose as: \[ f_b = 0.03\times E_i^{-0.8}, \] where the energy threshold ($$E_i$$) is measured in megatons.

Input

The three parameters: $$\Delta_t$$, $$P_i$$ and $$E_i$$, in that order and on three separate lines.

Output

The value of the Palermo Scale.

Example

Input:

10
0.5
20

Output:

1.26267274615