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>
#include <iostream>
#include <math.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 tmp = 0;
    bool can = true;
    for (int i=0; i < N; i++) {
        int n = i + 1;
        if (n != vec[i]) {
            tmp = vec[i];
            if (vec[tmp-1] != n) {
                can = false;
            }
        }
    }

    if (can) {
        cout << "YES" << endl;
    } else {
        cout << "NO" << endl;
    }

    return 0;
}