Description

Tom_nik and Uurist are playing a game on an $n\times m$ board. Initially the board is empty. First, Uurist places $k$ stones on the board, and then Tom_nik will destroy all the stones. However, for one operation, Tom_nik can only destroy stones that share a row or column.

Uurist will destroy the stones using the minimum number of operations. However, Tom_nik wants to maximize the number of operations Uurist will take by placing the stone in a proper way. You need to give him a specific placement such that Tom_nik's goal will be achieved.

Note that Uurist has to destroy all of the stones.

Input Format

This task contains multiple testcases. For each test, the first line of the input contains an integer $T$, indicating the number of testcases.

Then $T$ lines follow, each line containing three integers $n,m,k$.

Output Format

For each test case, output $n$ lines containing $nm$ characters, indicating your answer: the character on the $i$-th line and $j$-th column should be "$\texttt S$" (withut quotes), if you think you should place a stone on this grid; otherwise it should be "$\texttt .$" (without quotes).

You should guarantee that the number of grids with $\texttt S$ on it is $k$. If there are multiple answers, print any.

2
3 5 2
5 4 7

S....
....S
.....
S..S
...S
S.S.
...S
.S..

Hint

Subtasks are used in this problem.

Subtask 1 ($20$ points): it is guaranteed that $k \leq \min(n,m)$.
Subtask 2 ($12$ points): it is guaranteed that $n = 2$.
Subtask 3 ($18$ points): it is guaranteed that $T,n,m \leq 10$.
Subtask 4 ($20$ points): it is guaranteed that $T \leq 10$, $n,m \leq 300$.
Subtask 5 ($30$ points): No special constraint.

For all tests, it is guaranteed that $1 \leq T \leq 10^4$, $1 \leq n,m \leq 2 \times 10^3$, $0 \leq k \leq nm$, the sum of $nm$ over all test cases does not exceed $5\times 10^6$.