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

typedef long long ll;
typedef unsigned long long llu;

int main(int argc, char *argv[]) {
  ll N;
  cin >> N;

  vector<ll> p(N);
  vector<ll> orig(N);
  for (ll i = 0; i < N; ++i) {
    cin >> p[i];
  }
  orig = p;

  sort(p.begin(), p.end());

  ll diff = 0;
  for (ll i = 0; i < N; ++i) {
    if (p[i] != orig[i]) {
      diff++;
    }
  }
  
  if (diff > 2) {
    cout << "NO" << endl;
  } else {
    cout << "YES" << endl;
  }

  return 0;
}