Problem:
Score : 200 points

Problem Statement

Determine if an N-sided polygon (not necessarily convex) with sides of length L_1, L_2, ..., L_N can be drawn in a two-dimensional plane.

You can use the following theorem:

Theorem: an N-sided polygon satisfying the condition can be drawn if and only if the longest side is strictly shorter than the sum of the lengths of the other N-1 sides.

Constraints

All values in input are integers.

3 \leq N \leq 10

1 \leq L_i \leq 100

Input

Input is given from Standard Input in the following format:

N
L_1 L_2 ... L_N

Output

If an N-sided polygon satisfying the condition can be drawn, print Yes; otherwise, print No.

Sample Input 1

4
3 8 5 1

Sample Output 1

Yes

Since 8 < 9 = 3 + 5 + 1, it follows from the theorem that such a polygon can be drawn on a plane.

Sample Input 2

4
3 8 4 1

Sample Output 2

No

Since 8 \geq 8 = 3 + 4 + 1, it follows from the theorem that such a polygon cannot be drawn on a plane.

Sample Input 3

10
1 8 10 5 8 12 34 100 11 3

Sample Output 3

No

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

{-# OPTIONS_GHC -O2 -funbox-strict-fields #-}
import qualified Data.ByteString.Char8 as B
import           Data.Char             (isSpace)
import qualified Data.Vector.Unboxed   as V

main :: IO ()
main = do
  n <- readLn
  ls <- V.unfoldrN n parseInt <$> B.getLine
  putStrLn $ if solve n ls then "Yes" else "No"

solve :: Int -> V.Vector Int -> Bool
solve _ ls = m < V.sum (V.take i ls) + V.sum (V.drop (i + 1) ls)
  where i = V.maxIndex ls
        m = ls V.! i

parseInt :: B.ByteString -> Maybe (Int, B.ByteString)
parseInt = B.readInt . B.dropWhile isSpace