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>
#include <algorithm>

using namespace std;

int main(int argc, const char * argv[]) {
    int N = 0;
    cin >> N;

    vector<int> ps(N, 0);
    for(int i = 0; i < N; i++) {
        cin >> ps[i];
    }

    vector<bool> done(N, false);
    for(int i = 0; i < N; i++) {
        if(ps[i] == i+1) {
            continue;
        }

        // 以下で ps[i] と ps[ps[i]-1] を入れ替える

        if(done[i] || done[ps[i]-1]) {
            cout << "NO" << endl;
            return 0;
        }

        int swp_i1 = i;
        int swp_i2 = ps[i] - 1;
        swap(ps[swp_i1], ps[swp_i2]);
        if(ps[swp_i1] != swp_i1+1) {
            cout << "NO" << endl;
            return 0;
        }
        if(ps[swp_i2] != swp_i2+1) {
            cout << "NO" << endl;
            return 0;
        }

        done[swp_i1] = true;
        done[swp_i2] = true;
    }
    cout << "YES" << endl;
    return 0;
}

/**
 cheat sheet

 vector<int> v{ 1, 5, 8, 9, 6, 7, 3, 4, 2, 0 };
 sort(v.begin(), v.end());
 => 0 1 2 3 4 5 6 7 8 9

 vector<int> v{ 1, 5, 8, 9, 6, 7, 3, 4, 2, 0 };
 sort(v.begin(), v.end(), greater<int>());
 => 9 8 7 6 5 4 3 2 1 0

 struct A { int x, y; };
 bool comp(A i1, A i2) { return (i1.y < i2.y); }
 vector<A> v { { 6, 8 }, { 1, 9 }, { 2, 4 }, { 4, 7 } };
 sort(v.begin(), v.end(), comp);
 => [1, 9] [2, 4] [4, 7] [6, 8]

 */