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 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>

int f (const void *a, const void *b) {
    return *(int *)a - *(int*)b;
}

void swap(int *a, int *b) {
    int tmp = *a;
    *a = *b;
    *b = tmp;
}

int main() {
    int N;
    int *p = malloc(N * sizeof(int));
    int *sorted = malloc(N * sizeof(int));
    scanf("%d", &N);
    for (int i = 0; i < N; i++) {
        scanf("%d", &p[i]);
        sorted[i] = p[i];
    }
    qsort(sorted, N, sizeof(int), f);
    // 交換しないケース確認
    int same = 1;
    for (int k = 0; k < N; k++) {
        if (p[k] != sorted[k]) {
            same = 0;
            break;
        }
    }
    if (same == 1) {
        printf("YES\n");
        return 0;
    }


    for (int i = 0; i < N - 1; i++) {
        for (int j = i + 1; j < N; j++) {
            swap(&p[i], &p[j]);
            int same = 1;
            for (int k = 0; k < N; k++) {
                if (p[k] != sorted[k]) {
                    same = 0;
                    break;
                }
            }
            if (same == 1) {
                printf("YES\n");
                return 0;
            }
            swap(&p[i], &p[j]);
        }
    }

    printf("NO\n");
    return 0;
}