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>
#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;

int main() {
  int N,count=0,countt=0;cin>>N;
  vector<int> data(N);
  rep(i,N) cin>>data[i];
  rep(i,N-1){
    if(abs(data[i]-data[i+1])==1) count++;
  }
  bool hoge=false;
  if(count==N-1) cout << "YES" << endl;
  else{
    for(int i=0;i<N-1;i++){
      for(int j=i+1;j<N;j++){
        swap(data[i],data[j]);
        for(int k=0;k<N;k++){
          if(abs(data[k]-data[k+1])==1) countt++;
        }
        if(countt==N-1){
          cout << "YES" << endl;
          hoge=true;
          break;
        }
        swap(data[i],data[j]);
      }
      if(hoge) break;
    }
    if(!hoge) cout << "NO" << endl;
  }
}