Problem Description

Given a sequence $a$, determine if it is possible to sort the sequence in ascending order by swapping any two elements of the sequence exactly $N$ times. If it is possible, output YES; otherwise, output NO.

Input Format

None

Output Format

None

Sample Input and Output

Sample Input #1

5
3 1 5 4 2

Sample Output #1

YES

Sample Input #2

6
1 2 3 4 5 6

Sample Output #2

YES

Sample Input #3

7
7 6 5 4 3 2 1

Sample Output #3

YES

Sample Input #4

20
19 11 10 7 8 9 17 18 20 4 3 15 16 1 5 14 6 2 13 12

Sample Output #4

YES

Notes/Hints

Constraints

• $2 \leq N \leq 100,000$

见题面 Input 部分

见题面 Output 部分