Problem:
Score : 300 points

Problem Statement

Does \sqrt{a} + \sqrt{b} < \sqrt{c} hold?

Constraints

1 \leq a, b, c \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

a \ b \ c

Output

If \sqrt{a} + \sqrt{b} < \sqrt{c}, print Yes; otherwise, print No.

Sample Input 1

2 3 9

Sample Output 1

No

\sqrt{2} + \sqrt{3} < \sqrt{9} does not hold.

Sample Input 2

2 3 10

Sample Output 2

Yes

\sqrt{2} + \sqrt{3} < \sqrt{10} holds.

Solution in Haskell (GHC 8.8.3) (judge verdict: Wrong Answer)

main :: IO()
main = do
 [a,b,c] <- map read . words <$> getLine :: IO [Integer]
 -- 2 * sqrt(a * b) < c - a - b. Right hand is Integer.
 let rightHand = fromInteger (c - a - b)
 let aDouble = fromInteger a :: Double
 let bDouble = fromInteger b :: Double 
 let leftHand = (*) 2.0 $ sqrt $ aDouble * bDouble
 putStr $ if (leftHand < rightHand) then "Yes" else "No"