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Description

You are a fashion designer and you are excited about your fresh idea for a T-shirt. A T-shirt of size $n$ for your purposes is an $n \times n$ grid of unit squares. Your idea is to make such a T-shirt by sewing together T-patches. A T-patch consists of $3$ near-unit length segments connecting in a single point as shown:

Your design idea requires placing T-patches so that each side of each square of the T-shirt is covered by exactly one T-patch. Each T-patch can be rotated in any of the four orthogonal directions. For example, a T-shirt of size $2$ can be sewn as follows:

Given the size of the T-shirt $n$, find a correct way to sew it from T-patches or determine that it is impossible!

Input

The input contains a single integer $n$ ($1 \leq n \leq 1\,000$), the size of the T-shirt.

Output

The first line of output should contain "Yes" if there exists a required T-shirt of the given size, and "No" otherwise. In the first case you should then output $n+1$ lines of $n+1$ characters describing the design. The $j$-th character in the $i$-th line describes the intersection of the $i$-th horizontal and $j$-th vertical grid lines. For a T-patch, denote the shortest segment as its stem. If a center of a T-patch is located at that point output "D", "R", "U" or "L, if the stem points downward, rightward, upward or leftward, respectively. Otherwise, output the point character ".". If there are multiple solutions, output any of those.

2

3

Yes
.D.
R.L
.U.

No