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 Ruby (2.3.3) (judge verdict: Runtime Error)

n = gets().to_i
a = gets().split(' ').map(&:to_i)

def swappable(big, small)
    if (a[big - 1] < a[small] || big == 0) &&
      (a[small] < a[big + 1] || big == n - 1) &&
      a[small - 1] < a[big] && (a[big] < a[small + 1] || small == n - 1)
return true
    end
  return false
 
end


big = -1
small = -1
s = 0
for i in 0..(n-1)
  if i < n - 1
    if a[i] > a[i + 1]
      case s
      when 0 then
        s = 1
        big = i
      when 1 then
        s = 2
        small = i + 1
      when 2 then
        s = 3
        break # impossible
      end
    end
  end
end
  
  case s
when 0 then
  puts 'YES'
when 2 then
  if swappable(big, small)
    puts 'YES'
  else
    puts 'NO'
  end
else
  puts 'NO'
end