Write a program that reads angles in degrees and writes their sine. In order to solve this problem, you are requested to use the following Taylor series:

sinx = x − |
| + |
| − |
| + ⋯. |

Input

Input consists of angles in degrees in the [−180,180] interval.

Output

For each given angle, print its sine in a line.

Observation

The checker of this problem tolerates absolute errors up to 0.001.

Public test cases

**Input**

0 -180 180 45 60 -60 12.123 12.123001

**Output**

0 -2.3521e-16 2.3521e-16 0.707107 0.866025 -0.866025 0.210011 0.210011

Information

- Author
- Jordi Petit
- Language
- English
- Translator
- Jordi Petit
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++
- User solutions
- C++