SPOJ in Gyumri

   A belt drive consists of two pulleys of different radius (r₁ and r₂) connected by a belt of length l. The industry manufactures belts of different standard lengths, so the engi- neers often face a task of calculating the distance between the pulley centers given their radii and the belt length. There are several simple approximate methods to do this, which are precise enough for rough estimations. However, some engineering tasks require more precise data.

   Your task is to write a program that will calculate the distance a between the centers of the pulleys given their radii r₁ and r₂, and the length l of the belt.

Limitations

   1 ≤ r₁, r_{2 ≤} 1,000; 2π(r₁ + r₂) ≤ l ≤ 10,000.

Input

   The first line contains 3 space-delimited real numbers precise to four decimal places: r₁, r₂, l. Trailing zeros following the decimal point may be omitted.

Output

   The output file should contain a single real number, the center-to-center distance a. The answer must be precise to four decimal places.

Example