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 7.10.3) (judge verdict: Wrong Answer)

import Control.Monad
-- 時刻の差分 >= xの差 + yの差 AND 時刻の差分 と xの差 + yの差の遇機が一致

analyze :: [(Integer, Integer, Integer)] -> (Integer, Integer, Integer) -> Bool
analyze [] _ = True
analyze ((time, x, y):rem) (prtime, prx, pry) =
  (time - prtime >= dx + dy &&
    (time - prtime) `mod` 2 == (dx + dy) `mod` 2) &&
    analyze rem (time, x, y)
  where dx = abs $ x - prx; dy = abs $ y - pry
  
main = do
  [a, b, c] <- (map read . words <$> getLine :: IO [Integer])
  let r = c - a - b
  let res = r * r > a * b * 4
  putStrLn $ if res then "Yes" else "No"