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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>

using namespace std;

int main() {
  int n;
  cin >> n;
  vector<int> p(n + 2);
  // sentinels
  p[0] = 0;
  p[n + 1] = n + 1;
  for (int i = 1; i <= n; i++) {
    cin >> p[i];
  }
  int c = 0;
  int i = 0;
  int j = 0;
  for (int k = 1; k < n; k++) {
    if (p[k] < p[k + 1]) {
      continue;
    }
    if (c == 0) {
      i = k;
    } else if (c == 1) {
      j = k + 1;
    } else if (c == 2) {
      cout << "NO" << endl;
      return 0;
    }
    c++;
  }
  bool ok = c == 0 || ((p[i - 1] < p[j] && p[j] < p[i + 1]) &&
                       (p[j - 1] < p[i] && p[i] < p[j + 1]));
  cout << (ok ? "YES" : "NO") << endl;
  return 0;
}