Problem:
Score : 200 points

Problem Statement

We have a sequence p = {p_1,\ p_2,\ ...,\ p_N} which is a permutation of {1,\ 2,\ ...,\ N}.

You can perform the following operation at most once: choose integers i and j (1 \leq i < j \leq N), and swap p_i and p_j. Note that you can also choose not to perform it.

Print YES if you can sort p in ascending order in this way, and NO otherwise.

Constraints

All values in input are integers.

2 \leq N \leq 50

p is a permutation of {1,\ 2,\ ...,\ N}.

Input

Input is given from Standard Input in the following format:

N
p_1 p_2 ... p_N

Output

Print YES if you can sort p in ascending order in the way stated in the problem statement, and NO otherwise.

Sample Input 1

5
5 2 3 4 1

Sample Output 1

YES

You can sort p in ascending order by swapping p_1 and p_5.

Sample Input 2

5
2 4 3 5 1

Sample Output 2

NO

In this case, swapping any two elements does not sort p in ascending order.

Sample Input 3

7
1 2 3 4 5 6 7

Sample Output 3

YES

p is already sorted in ascending order, so no operation is needed.

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

import Data.Bool

main :: IO ()
main = do
  (n:ps) <- readParams
  putStrLn $ solve [1..n] ps

readParams :: Read a => IO [a]
readParams = map read . words <$> getContents

solve :: [Int] -> [Int] -> String
solve = format .: solve'

format :: Bool -> String
format = bool "NO" "YES"

solve' :: [Int] -> [Int] -> Bool
solve' = (<=2) .: length .: filter (/=0) .: zipWith (-)

infixr 8 .:
(.:) :: (c -> d) -> (a -> b -> c) -> a -> b -> d
(f .: g) x y = f $ g x y