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 Python (3.4.3) (judge verdict: Runtime Error)

def check_list_sorted(N, p_list):
    cnt = 0
    for i in range(N-1):
        if p_list[i] < p_list[i+1]:
            cnt += 1
    if cnt == N-1:
        return True
    else:
        return False

def swap_list(N, p_list):
    for i in range(N-1):
        if p_list[i] > p_list[i+1]:
            if i == 0 and N == 2:
                idx = 1
            else:
                idx = p_list.index(p_list[i+1]-1)
            p_list[i], p_list[idx] = p_list[idx], p_list[i]
            break
    return p_list

N = int(input())
p_list = list(map(int, input().split()))
if check_list_sorted(N, p_list):
    print("YES")
else:
    new_p_list = swap_list(N, p_list)
    if check_list_sorted(N, new_p_list):
        print("YES")
    else:
        print("NO")