Problem: We have a grid with H rows and W columns of squares. We will represent the square at the i-th row from the top and j-th column from the left as (i,\ j). Also, we will define the distance between the squares (i_1,\ j_1) and (i_2,\ j_2) as |i_1 - i_2| + |j_1 - j_2|.

Snuke is painting each square in red, yellow, green or blue. Here, for a given positive integer d, he wants to satisfy the following condition:

* No two squares with distance exactly d have the same color.



Find a way to paint the squares satisfying the condition. It can be shown that a solution always exists.

Constraints

* 2 ≤ H, W ≤ 500
* 1 ≤ d ≤ H + W - 2

Input

Input is given from Standard Input in the following format:


H W d


Output

Print a way to paint the squares satisfying the condition, in the following format. If the square (i,\ j) is painted in red, yellow, green or blue, c_{ij} should be `R`, `Y`, `G` or `B`, respectively.


c_{11}c_{12}...c_{1W}
:
c_{H1}c_{H2}...c_{HW}

Output

Print a way to paint the squares satisfying the condition, in the following format. If the square (i,\ j) is painted in red, yellow, green or blue, c_{ij} should be `R`, `Y`, `G` or `B`, respectively.


c_{11}c_{12}...c_{1W}
:
c_{H1}c_{H2}...c_{HW}

Examples

Input

2 2 1


Output

RY
GR


Input

2 3 2


Output

RYB
RGB

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.PrintWriter;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		
		int H = sc.nextInt();
		int W = sc.nextInt();
		int d = sc.nextInt();
		char[] c = "RYGB".toCharArray();
		
		for(int i=0; i<H; i++) {
			for(int j=0; j<W; j++) {
				pw.print(d%2==0 ? c[( (i+j)/2/(d/2) + (i-j+W)/2/(d/2)*2)%4]: c[(i+j)%4]);
			}
			pw.println();
		}

		sc.close();
		pw.close();
	}
}