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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

int main() {
  int N;
  cin >> N;

  vector<int> vec(N);
  for (int i = 0 ; i<N; i++) {
    cin >> vec.at(i);
  }
  
  //int num1, ite1, num2, ite2, count = 0;
  int ite1, ite2, count = 0;
  for (int i = 0 ; i<(N-1); i++) {
    if (vec.at(i)>vec.at(i+1)) {
      count++;
      if (count == 1) {
        //num1 = vec.at(i);
        ite1 = i;
      }
      else if (count == 2) {
        //num2 = vec.at(i+1);
        ite2 = i+1;
      }
    }
  }
  if (count == 2) {
    swap(vec.at(ite1),vec.at(ite2));
  }

  string ans;
  if (count == 2) {
    for (int i = 0 ; i<(N-1); i++) {
      if (vec.at(i)>vec.at(i+1)) {
        count++;
      }
    }
    if (count > 0)
      ans = "NO";
    else
      ans = "YES";
  }
  else if (count == 0)
    ans = "YES";
  else
    ans = "NO";
  
  cout << ans << endl;
}