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 test
  implicit none
  integer :: n, i, flag, tmp
  integer, dimension ( : ), allocatable :: p
  
  read ( unit = *, fmt = * ) n

  allocate ( p ( 1:n ) )

  read ( unit = *, fmt = * ) p ( 1:n )
  
  flag = 0

  do i = 1, n

     if ( p ( i ) == i ) then

        continue
     
     else if ( p ( i ) /= i .and. p ( p ( i ) ) == i ) then

        tmp = p ( i )

        p ( i ) = p ( p ( i ) )

        p ( tmp ) = tmp

        flag = flag + 1

     else

        write ( unit = *, fmt = '(a2)' ) 'NO'
        
        stop
        
     end if

     if ( flag > 1 ) then

        write ( unit = *, fmt = '(a2)' ) 'NO'

        stop

     else

        write ( unit = *, fmt = '(a3)' ) 'YES'

        stop

     end if

  end do
  
end program test