Ada Rooks 2

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### Read problem statements in [Hindi](http://www.codechef.com/download/translated/MAY19/hindi/ADAROKS2.pdf), [Bengali](http://www.codechef.com/download/translated/MAY19/bengali/ADAROKS2.pdf), [Mandarin Chinese](http://www.codechef.com/download/translated/MAY19/mandarin/ADAROKS2.pdf), [Russian](http://www.codechef.com/download/translated/MAY19/russian/ADAROKS2.pdf), and [Vietnamese](http://www.codechef.com/download/translated/MAY19/vietnamese/ADAROKS2.pdf) as well. In order to beat AlphaZero, Chef Ada is improving her chess calculation skills. Today, Ada 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 $(r, c)$. Ada 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 $r_1$, $c_1$, $r_2$, $c_2$ ($r_1 \neq r_2, c_1 \neq c_2$) such that there are rooks on squares $(r_1, c_1)$, $(r_1, c_2)$, $(r_2, c_1)$ and $(r_2, c_2)$.  The number of rooks is at least $8N$. Help Ada 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 description of $T$ test cases follows.  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. ### Constraints  $100 \le N \le 1,000$  the sum of $N^2$ over all test cases does not exceed $5 \cdot 10^6$ ### Subtasks **Subtask #1 (20 points):** $N \le 200$ **Subtask #2 (80 points):** original constraints ### Example Input ``` 1 100 ``` ### Example Output ``` OO.O [96 characters follow] O... [96 characters follow] ..O. [96 characters follow] O... [96 characters follow] [96 lines follow] ``` ### Explanation The output depicts the top left $4 \times 4$ square on the board. The rest of the board is cropped.Author:  alei 
Tags  alei 
Date Added:  18042019 
Time Limit:  4 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, PYP3, CLOJ, R, COB, FS 
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