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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(defun split (x str)
  (let ((pos (search x str))
        (size (length x)))
    (if pos
      (cons (subseq str 0 pos)
            (split x (subseq str (+ pos size))))
      (list str))))

(setq *n* (read))
(setq *ps* (mapcar #'parse-integer (split " " (read-line))))

(defun count-transposition (l i)
  (if (equal l nil)
    0
    (if (equal (car l) i)
      (count-transposition (cdr l) (1+ i))
      (1+ (count-transposition (cdr l) (1+ i))))))

(format t "~a~%"
 (if (<= (count-transposition *ps* 1) 2)
   "YES"
   "NO"))