PYTHON CODE: In order to beat AlphaZero, Grandmaster Hikaru is improving her chess calculation skills. Today, Hikaru took a big chessboard with N rows (numbered 1 through N) and N columns (numbered 1 through N). Let's denote the square in row r and column c of the chessboard by (r,c). Hikaru wants to place some rooks on the chessboard in such a way that the following conditions are satisfied: • Each square of the board contains at most one rook. • There are no four rooks forming a rectangle. Formally, there should not be any four valid integers r1, c1, r2, c2 (≠r2,c1≠c2) such that there are rooks on squares (r1,c1), (r1,c2 (r2,c1)and (r2,c2). • The number of rooks is at least 8N. Help Hikaru find a possible distribution of rooks. If there are multiple solutions, you may find any one. It is guaranteed that under the given constraints, a solution always exists. Input The first line of the input contains a single integer T denoting the number of test cases. The first and only line of each test case contains a single integer N. Output For each test case, print N lines. For each valid i, the i-th of these lines should contain a single string with length N describing row i of the chessboard; for each valid j, the j-th character of this string should be 'O' if there is a rook in the square (i,j) or '.' if this square is empty.
PYTHON CODE:
In order to beat AlphaZero, Grandmaster Hikaru is improving her chess calculation skills.
Today, Hikaru took a big chessboard with N rows (numbered 1 through N) and N columns (numbered 1 through N). Let's denote the square in row r and column c of the chessboard by (r,c). Hikaru wants to place some rooks on the chessboard in such a way that the following conditions are satisfied:
• Each square of the board contains at most one rook.
• There are no four rooks forming a rectangle. Formally, there should not be any four valid integers r1, c1, r2, c2 (≠r2,c1≠c2) such that there are rooks on squares (r1,c1), (r1,c2 (r2,c1)and (r2,c2).
• The number of rooks is at least 8N.
Help Hikaru find a possible distribution of rooks. If there are multiple solutions, you may find any one. It is guaranteed that under the given constraints, a solution always exists.
Input
The first line of the input contains a single integer T denoting the number of test cases. The first and only line of each test case contains a single integer N.
Output
For each test case, print N lines. For each valid i, the i-th of these lines should contain a single string with length N describing row i of the chessboard; for each valid j, the j-th character of this string should be 'O' if there is a rook in the square (i,j) or '.' if this square is empty.
Sample Run
Input
1
5
Output
O.O..
OO.O.
.OO.O
..OO.
...OO
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