Problem:
Score : 700 points

Problem Statement

There are N cats.
We number them from 1 through N.

Each of the cats wears a hat.
Cat i says: "there are exactly a_i different colors among the N - 1 hats worn by the cats except me."

Determine whether there exists a sequence of colors of the hats that is consistent with the remarks of the cats.

Constraints

2 ≤ N ≤ 10^5

1 ≤ a_i ≤ N-1

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print Yes if there exists a sequence of colors of the hats that is consistent with the remarks of the cats; print No otherwise.

Sample Input 1

3
1 2 2

Sample Output 1

Yes

For example, if cat 1, 2 and 3 wears red, blue and blue hats, respectively, it is consistent with the remarks of the cats.

Sample Input 2

3
1 1 2

Sample Output 2

No

From the remark of cat 1, we can see that cat 2 and 3 wear hats of the same color.
Also, from the remark of cat 2, we can see that cat 1 and 3 wear hats of the same color.
Therefore, cat 1 and 2 wear hats of the same color, which contradicts the remark of cat 3.

Sample Input 3

5
4 3 4 3 4

Sample Output 3

No

Sample Input 4

3
2 2 2

Sample Output 4

Yes

Sample Input 5

4
2 2 2 2

Sample Output 5

Yes

Sample Input 6

5
3 3 3 3 3

Sample Output 6

No

Solution in Haskell (GHC 7.10.3) (judge verdict: Runtime Error)

{-# LANGUAGE MultiWayIf #-}
import Data.List (sort,group)
import Control.Arrow ((&&&))

main = do
  n <- read <$> getLine :: IO Int
  as <- map (head&&&length).group.sort.map read.words <$> getLine :: IO [(Int,Int)]
  putStrLn $ case length as of
    1 -> let m = (fst.head) as
         in if | m == 1 -> "Yes"
               | m == n-1 -> "Yes"
               | n `div` m > 1 -> "Yes"
               | otherwise -> "No"
    2 -> let [(s,i),(t,j)] = as
         in if | s == t-1 && (n-i)`div`(s-i+1) > 1 -> "Yes"
               | otherwise -> "No"
    _ -> "No"