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Security Bijective Functions

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Now that we know about one-to-one functions, let's talk about onto functions and bijective functions.

A function is onto if and only if each element in the co-domain is the image of, at least, one element in the domain . That is:

If the function is both one-to-one and onto then is a bijection from to or, equivalently, is a bijective function.

In this task, you'll be given an integer and a function where . Determine whether the given function is a bijective function 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

On a single line, output "YES" if is bijective. Otherwise, output "NO".

Sample Input

3
1 2 3

Sample Output

YES

Explanation

Basically, this is the function .

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