1450C2 · Errich-Tac-Toe (Hard Version)

Problem: 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.

Input Format: 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 $300$.

Output Format: 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.

Note: 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.