The Arrhenius equation — called after the Swedish scientist Svante Arrhenius¹ — predicts the temperature dependence of chemical reaction rates. The reaction rate at a particular temperature is determined both by the activation energy of the reaction and the chance that molecules will collide. The mean amount of thermal energy that molecules at a particular temperature $$T$$ (expressed in Kelvin) possess equals $$R \cdot T$$, with $$R$$ referring to the Universal Gas Constant ($$8,314472\, \textrm{J}\textrm{K}^{-1}\textrm{mol}^{-1}$$). The fraction of molecules having enough energy to overcome the energy barrier — those containing more energy than the activation energy $$E_A$$, expressed in joule per mole — depends exponentially on the ratio of the activation energy to the thermal energy. As such, the Arrhenius equation is: \[k = Ae^{\frac{-E_A}{R \cdot T}}\] in which $$k$$ depicts the reaction rate for the considered reaction at a particular temperature, and $$A$$ the (reaction specific) pre-exponential factor. As a consequence, when elevating temperature or lowering the activation energy (for instance by adding a catalyst) the reaction rate will increase. For a particular reaction, both $$k$$ and $$A$$ must be experimentally determined.

Input

Three real numbers: the experimentally determined pre-exponential factor $$A$$, the activation energy $$E_A$$ and the temperature $$T$$ ( in Kelvin) for a particular reaction, each on a separate line.

Output

The reaction rate $$k$$ of the reaction characterized by the values read from the input. This reaction rate must be calculated according to the Arrhenius equation.

Example

Input:

5.4
120
293.15

Output:

5.140579988724816