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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<int, int>;

int main()
{
    int n;
    cin >> n;
    vector<int> p(n);
    rep(i, n) cin >> p[i];
    bool ok = true;
    rep(i, n - 1) if (p[i] > p[i + 1]) ok = false;
    if (ok)
    {
        cout << "YES" << endl;
        return 0;
    }
    rep(i, n)
    {
        rep(j, n)
        {
            if (p[i] > p[j])
            {
                swap(p[i], p[j]);
                ok = true;
                rep(k, n - 1) if (p[k] > p[k + 1]) ok = false;
                if (ok)
                {
                    cout << "YES" << endl;
                    return 0;
                }
                swap(p[i], p[j]);
            }
        }
    }
    cout << "NO" << endl;
    return 0;
}