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 8.8.3) (judge verdict: Accepted)

{-# LANGUAGE Strict #-}
import qualified Data.ByteString.Char8 as B
import qualified Data.Vector.Unboxed   as V

main :: IO ()
main = do
  n <- readLn
  ps <- readIntsLn
  putStrLn $ if solve n ps then "YES" else "NO"

solve :: Int -> V.Vector Int -> Bool
solve _ ps = l <= 2
  where l = V.length $ V.ifilter (\i x -> (i + 1) /= x) ps

readIntsLn :: IO (V.Vector Int)
readIntsLn = V.unfoldr (B.readInt . B.dropWhile (== ' ')) <$> B.getLine