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 Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

program main
  implicit none
  integer :: i, j, n
  logical :: ans
  integer, allocatable :: p(:), q(:)

  read *, n 
  allocate (p(n), q(n))
  read *, p
  q(:) = p(:)
  if (minval(q(2:n) - q(1:n-1)) > 0) ans = .true.
  do i = 1, n
    do j = i+1, n
      q(:) = p(:)
      q(i) = p(j)
      q(j) = p(i)
      if (minval(q(2:n) - q(1:n-1)) == 1 .and. maxval(q(2:n) - q(1:n-2)) == 1) ans = .true.
    end do
  end do
  if (ans) then
    print '(a)', 'YES'
  else
    print '(a)', 'NO'
  end if
end program