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.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

class Main {
	public static void main(String[] args) {
		new Main().run();
	}

	void run() {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[] P = new int[N];
		for (int i = 0; i < N; ++i) {
			P[i] = sc.nextInt();
			--P[i];
		}
		boolean ans = false;
		for (int i = 0; i < N; ++i) {
			for (int j = 0; j < N; ++j) {
				if (i != j) {
					P[i] ^= P[j];
					P[j] ^= P[i];
					P[i] ^= P[j];
				}
				boolean ok = true;
				for (int k = 0; k < N; ++k) {
					ok &= P[k] == k;
				}
				ans |= ok;
				if (i != j) {
					P[i] ^= P[j];
					P[j] ^= P[i];
					P[i] ^= P[j];
				}
			}
		}
		System.out.println(ans ? "YES" : "NO");
	}

	void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}

}