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  1. Prepare
  2. Security
  3. Functions
  4. Security Involution

Security Involution

Consider a function where is any set, and is a bijection.

Now, if then is called an involution. In other words, a function is called an involution if

In this task you're given a permutation .

Determine whether is an involution or not.

Constraints

Input Format

There are lines in the input.
The first line contains a single positive integer .
The second line contains space separated integers, the values of , respectively.

Output Format

Output "YES" if is an involution. Otherwise, output "NO".

Sample Input

2
2 1

Sample Output

YES

Explanation

Since, and and .

Hence, is an involution.