Errich-Tac-Toe (Hard Version)

题意翻译

给定一张 $n$ 行 $n$ 列的棋盘，每个格子可能是空的或包含一个标志，标志有 $\text{X}$ 和 $\text{O}$ 两种。 如果有三个相同的标志排列在一行或一列上的三个连续的位置，则称这个棋盘是一个 **胜局**， 否则称其为 **平局**。  例如，上图第一行的局面都是胜局，而第二行的局面都是平局。 在一次操作中，你可以将一个 $\text X$ 改成 $\text O$，或将一个 $\text O$ 改成 $\text X$。 设棋盘中标志的总数为 $k$，你需要用不超过 $\lfloor \frac{k}{3}\rfloor$ 次操作把给定的局面变成平局。 $1\leq n\leq 300$。

题目描述

The only difference between the easy and hard versions is that tokens of type O do not appear in the input of the easy version. Errichto gave Monogon the following challenge in order to intimidate him from taking his top contributor spot on Codeforces. In a Tic-Tac-Toe grid, there are $ n $ rows and $ n $ columns. Each cell of the grid is either empty or contains a token. There are two types of tokens: X and O. If there exist three tokens of the same type consecutive in a row or column, it is a winning configuration. Otherwise, it is a draw configuration.  The patterns in the first row are winning configurations. The patterns in the second row are draw configurations. In an operation, you can change an X to an O, or an O to an X. Let $ k $ denote the total number of tokens in the grid. Your task is to make the grid a draw in at most $ \lfloor \frac{k}{3}\rfloor $ (rounding down) operations. You are not required to minimize the number of operations.

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1\le t\le 100 $ ) — the number of test cases. The first line of each test case contains a single integer $ n $ ( $ 1\le n\le 300 $ ) — the size of the grid. The following $ n $ lines each contain a string of $ n $ characters, denoting the initial grid. The character in the $ i $ -th row and $ j $ -th column is '.' if the cell is empty, or it is the type of token in the cell: 'X' or 'O'. It is guaranteed that not all cells are empty. The sum of $ n $ across all test cases does not exceed $ 300 $ .

输出格式

For each test case, print the state of the grid after applying the operations. We have proof that a solution always exists. If there are multiple solutions, print any.

输入输出样例

输入样例 #1

3
3
.O.
OOO
.O.
6
XXXOOO
XXXOOO
XX..OO
OO..XX
OOOXXX
OOOXXX
5
.OOO.
OXXXO
OXXXO
OXXXO
.OOO.

输出样例 #1

.O.
OXO
.O.
OXXOOX
XOXOXO
XX..OO
OO..XX
OXOXOX
XOOXXO
.OXO.
OOXXO
XXOXX
OXXOO
.OXO.

说明

In the first test case, there are initially three 'O' consecutive in the second row and the second column. By changing the middle token to 'X' we make the grid a draw, and we only changed $ 1\le \lfloor 5/3\rfloor $ token. In the second test case, the final grid is a draw. We only changed $ 8\le \lfloor 32/3\rfloor $ tokens. In the third test case, the final grid is a draw. We only changed $ 7\le \lfloor 21/3\rfloor $ tokens.

题意翻译

给定一张 $n$ 行 $n$ 列的棋盘，每个格子可能是空的或包含一个标志，标志有 $\text{X}$ 和 $\text{O}$ 两种。 如果有三个相同的标志排列在一行或一列上的三个连续的位置，则称这个棋盘是一个 **胜局**， 否则称其为 **平局**。  例如，上图第一行的局面都是胜局，而第二行的局面都是平局。 在一次操作中，你可以将一个 $\text X$ 改成 $\text O$，或将一个 $\text O$ 改成 $\text X$。 设棋盘中标志的总数为 $k$，你需要用不超过 $\lfloor \frac{k}{3}\rfloor$ 次操作把给定的局面变成平局。 $1\leq n\leq 300$。