As Beremiz reminded a sheikh, this is the famous Pythagoras’ theorem:

*“In any right triangle,
the square of the hypotenuse
equals the sum of the squares of the legs.”*

Input

Input consists of several cases,
each with three natural numbers between 1 and 10^{4}.

Output

Print a line for every case. If the three given numbers can be the sides of a right triangle, print its area (it will always be integer). Otherwise, if they can be the sides of a non-degenerate triangle (i.e., with strictly positive area), print “yes”. Otherwise, print “no”.

Public test cases

**Input**

3 4 5 10 17 10 100 1 2 5 6 11

**Output**

6 yes no no

Information

- Author
- Salvador Roura
- Language
- English
- Translator
- Salvador Roura
- Original language
- Spanish
- Other languages
- Spanish
- Official solutions
- C++
- User solutions
- C++