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           Control.Monad
import qualified Data.ByteString.Char8 as BS
import           Data.List
import           Data.Maybe

readInts :: IO [Int]
readInts = map (fst . fromJust . BS.readInt) . BS.words <$> BS.getLine

main = do
  _ <- BS.readInt <$> BS.getLine
  nums <- readInts
  putStrLn $ solve nums

solve :: [Int] -> String
solve nums
  | ans < 3 = "YES"
  | otherwise = "NO"
  where
    nums' = sort nums
    zipped = zip nums nums'
    ans = sum $ map f zipped
    f (x, y)
      | x == y = 0
      | otherwise = 1