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 <iostream>
#include <vector>
int main(){
    int N;
    std::cin >> N;
    std::vector<int> p(N);
    for(int i = 0; i < N; i++){
        std::cin >> p[i];
    }
    bool ju = false;
    for(int i = 0; i<N;i++){
        if(i+1 != p[i]){
         ju = true;
         break;   
        }
    }
    if(!ju){
        std::cout << "YES" << std::endl;
        return 0;
    }
    for(int i = 0; i < N; i++){
        for(int j = i + 1; j < N; j++){
            if(p[i]+1 == p[i+1]) break;
            if(p[i+1]-1 == p[j]){
                std::swap(p[i+1],p[j]);
                bool jud = false;
                for(int i = 0; i<N;i++){
                    if(i+1 != p[i]){
                        jud = true;
                        break;   
                    }
                }
                if(!jud){
                    std::cout << "YES" << std::endl;
                    return 0;
                }
                std::cout << "NO" << std::endl;
                return 0;
            }
        }
    }
    std::cout << "NO" << std::endl;
    return 0;
}