G. Geometric Gridlock
time limit per test
1 second
memory limit per test
1024 megabytes
input
standard input
output
standard output

Pentominous is a grid logic puzzle based on the twelve pentominoes. A pentomino is a polygon formed by connecting five equal-sized squares edge to edge.

The twelve pentominoes (up to mirroring and rotations) and their names.

The goal of this puzzle is to divide a grid into regions of size $$$5$$$ (that is, pentominoes), so that no two regions that share a side have the same shape. You are allowed to rotate and mirror the pentominoes, but such rotations and reflections count as the same shape. The twelve possible shapes can be seen in Figure above.

In a normal Pentominous puzzle, the player is given some pre-filled cells, for which the shape of their region is already predetermined. In this problem, you are working with a completely blank grid of dimensions $$$h\times w$$$, and your task is to create any valid arrangement of pentominoes.

Input

The input consists of:

  • One line with two integers $$$h$$$ and $$$w$$$ ($$$1 \le h,w \le 100$$$), the height and width of the grid.
Output

If there is no valid $$$h\times w$$$ Pentominous grid, output "no". Otherwise, output "yes", followed by $$$h$$$ lines of width $$$w$$$ each, a possible grid using the letters from the problem statement. If there is more than one solution, any one of them will be accepted.

Examples
Input
3 5
Output
yes
UUXUU
UXXXU
UUXUU
Input
2 10
Output
yes
LLLLNNNPPP
LIIIIINNPP
Input
99 17
Output
no
Input
6 10
Output
yes
IPPYYYYVVV
IPPXYLLLLV
IPXXXFZZLV
ITWXFFFZUU
ITWWNNFZZU
TTTWWNNNUU
Input
1 5
Output
yes
IIIII
Note

Illustration of Sample Output 1.

Illustration of Sample Output 2.

Illustration of Sample Output 4.