Parity Chessboard

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

For an $r$-by-$c$ grid, number rows and columns starting from 1. Print X at $(i,j)$ if $i+j$ is even, and O otherwise. Print $r$ rows of $c$ consecutive characters. The upper-left cell is X.

Input

One line contains integers $r,c$.

Output

Print $r$ lines, each containing $c$ characters X or O.

Subtasks

• Subtask 1 (20%): $1\le r,c\le 2$.

• Subtask 2 (30%): $1\le r,c\le 8$.

• Subtask 3 (50%): $1\le r,c\le 30$.

Examples

Example 1

Input:

2 3

Output:

XOX
OXO

Explanation:

The upper-left coordinate sum is 2, an even number; parity alternates across rows and columns. For this sample, the input is 2 3; the displayed rows follow these rules exactly.

Example 2

Input:

1 1

Output:

X

Explanation:

The upper-left coordinate sum is 2, an even number; parity alternates across rows and columns. For this sample, the input is 1 1; the displayed rows follow these rules exactly.