Fujiwara Wants to See Couples

Fujiwara really likes couples.

There are $B$ boys and $G$ girls to place in an $N\times N$ grid. It is guaranteed that $B+G=N^2$, and exactly one student must be placed in each cell.

Two students meet if they have different genders and their cells share an edge. The number of meetings is the number of such pairs of cells. Count each pair once; cells that share only a corner do not count.

Represent a boy by B and a girl by G, and output a grid that maximizes the number of meetings.

The input is given in the following format.

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$

For each test case, output the arrangement in $N$ lines. Each line must be a string of length $N$ containing only B and G. Each character represents the gender of the student placed in that cell.

The grid must contain exactly $B$ occurrences of B and $G$ occurrences of G. The number of meetings must be as large as possible. If there are multiple optimal arrangements, output any of them.

Output the grids in the order the test cases appear in the input, without separators or blank lines between them.

• $1\leq T\leq 1000$.
• $2\leq N\leq 2000$.
• $0\leq B,G\leq N^2$.