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>
#include <math.h>
#include <cmath>
using namespace std;
bool is_int_lround(double x){
  return std::lround(x)==x;
}
int main(){
  int N;
  cin>>N;
  vector<int> PPP(N);
  for(int i=0; i<N ;i++){
    cin>> PPP.at(i) ;
  }
  bool ans =true;
  int count=0;
  for(int i=0;i<N;i++){
   if(PPP.at(i)!=i+1){
     if(PPP.at(PPP.at(i)-1) !=i+1 ){
       ans =false;
       break;
     }
     else if(PPP.at(PPP.at(i)-1) ==i+1 ){
       count ++;
     }
   }
  }
  if(count ==2){
    cout <<"YES"<<endl;
  }
  else if(ans && count ==0){
    cout <<"YES"<<endl;
  }
  else{
    cout<<"NO"<<endl;
  }
}