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 PYTHON3):

Solution:
h,w,d = map(int,input().split())
if d%2:
  for i in range(h):
    for j in range(w):
      if (i+j)%2:
        print("R",end="")
      else:
        print("G",end="")
    print()
else:
  cell = [["A" for i in range(2*d)] for j in range(2*d)]
  for i in range(d):
    for j in range(d):
      if (i+j)%2 == (d//2-1)%2:
        if abs(i-j) <= d//2-1 and d//2-1 <= i+j <= (d//2-1)*3:
          cell[i][j] = "R"
      elif j and cell[i][j-1] == "R":
        cell[i][j] = "R"
  for i in range(2*d):
    for j in range(2*d):
      if cell[(i-d)%(2*d)][(j-d)%(2*d)] == "R":
        cell[i][j] = "R"
      elif cell[(i-d//2)%(2*d)][(j-d//2)%(2*d)] == "R" or cell[(i+d//2)%(2*d)][(j+d//2)%(2*d)] == "R" :
        cell[i][j] = "G"
      elif cell[(i-d)%(2*d)][j] == "R" or cell[i][(j-d)%(2*d)] == "R":
        cell[i][j] = "B"
      elif cell[i][j] == "A":
        cell[i][j] = "Y"
  ans = [["A" for i in range(w)] for j in range(h)]
  for i in range(h):
    for j in range(w):
      x = cell[i%(2*d)][j%(2*d)]
      ans[i][j] = x
    print(*ans[i],sep="")