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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

  public static void main(String[] args) {
    Scanner scan = new Scanner(System.in);
       
    int n = scan.nextInt();
    int[] p = new int[n];
    
    for (int i = 0; i < n; i++) {
      p[i] = scan.nextInt();
    }
    
    for (int k = 0; k < n - 1; k++) {
    	if (p[k] > p[k+1]) {
    		break;
    	} else if (k == (n - 2)) {
    		System.out.print("YES");
    		return;
    	}
    }
    
    int[] q = new int[n];
    
    for (int i = 0; i < n - 1; i++) {    
      for (int j = i + 1; j < n; j++) {
    	for (int k = 0; k < n; k++) {
			 q[k] = p[k];
		}
		q[i] = p[j];
		q[j] = p[i];
		
		for (int k = 0; k < n - 1; k++) {
			if (q[k] > q[k+1]) {
				break;
			} else if (k == (n - 2)) {
				System.out.print("YES");
				return;
			}
		}
      }
    }
    
    System.out.print("NO");
    return;
  }
}