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>
using namespace std;
#define what_is(x) cerr << #x << " is " << x << endl;
#define IOS ios::sync_with_stdio(false); cin.tie(0);
#define st first
#define nd second
#define endl '\n'

typedef long long ll;
typedef pair<int,int> pii;
const int N = 50+5;
const int INF = 1e9;
const int MOD = 1e9+7;

int n;
vector<int> a;

bool ok(int i, int j){
	vector<int> b(a);
	swap(b[i], b[j]);
	for(int k=0; k<n; k++){
		if (b[k] == k+1) continue;
		return false;
	}
	return true;
}
int main()
{
	IOS
	// freopen("input.txt", "r", stdin);
	cin >> n;
	a.resize(n);
	for(int i=0; i<n; i++) cin >> a[i];
	for(int i=0; i<n; i++){
		for(int j=i+1; j<n; j++){
			if (ok(i,j)) return 0*puts("YES");
		}
	}
	puts("NO");
	return 0;
}