Grid Number Arrangement Parity

You are given a square grid of side length \(n\). You need to fill the grid with the numbers from \(1\) to \(n^2\) such that:

• The sum of the numbers in every row is odd.
• The sum of the numbers in every column is even.

Before actually arranging the numbers, you are required to check whether any such arrangement exists. If it exists, output Yes; otherwise, output No.

Note: You are not required to provide the actual arrangement, only to determine if one exists.

Hint: Consider the parity of the total sum computed by rows and columns.

inputFormat

The input consists of a single integer \(n\) representing the side length of the grid, where \(1 \le n \le 10^5\).

outputFormat

Output a single line: Yes if there exists an arrangement satisfying the conditions, or No otherwise.

sample

2

Yes