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 Scala (2.11.7) (judge verdict: Accepted)

object Main {

  def main(args: Array[String]): Unit = {
    val sc = new java.util.Scanner(System.in)

    val N = sc.nextInt()
    val sortedP = (1 to N).toArray
    val P = Array.fill(N)(sc.nextInt())

    def check(a: Array[Int], b: Array[Int], ii: Int, jj: Int): Boolean = {
      var i = 0
      var r = true
      while (i < N) {
        r &&= {
          if (i == ii) a(jj) == b(i)
          else if (i == jj) a(ii) == b(i)
          else a(i) == b(i)
        }
        i += 1
      }
      r
    }

    val results = for {
      i <- 0 until N
      j <- 0 until N
    } yield check(P, sortedP, i, j)
    if (results.exists(identity) || check(P, sortedP, 0, 0)) {
      println("YES")
    } else println("NO")
  }

}