0 or 1 Swap

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.

Examples

Input

5 5 2 3 4 1

Output

YES

Input

5 2 4 3 5 1

Output

NO

Input

7 1 2 3 4 5 6 7

Output

YES

inputFormat

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

outputFormat

Output

Print YES if you can sort p in ascending order in the way stated in the problem statement, and NO otherwise.

Examples

Input

5 5 2 3 4 1

Output

YES

Input

5 2 4 3 5 1

Output

NO

Input

7 1 2 3 4 5 6 7

Output

YES

样例

5
2 4 3 5 1

NO