Mine Sweeper

A mine-sweeper map can be expressed as an $r\times c$ grid, and each cell of the grid is either mine cell or non-mine cell. A mine cell has no number on it, while a non-mine cell has a number, the number of mine cells that share at least one common point with the cell, on it. Following is a $16\times 30$ mine-sweeper map, where flag cells denotes mine cells while blank cells denotes non-mine cells with number 0 on them.



Given an integer $S$, construct a mine-sweeper map of $r, c$ both not exceeding 25, whose sum of numbers on non-mine cells exactly equals $S$. If multiple solutions exist, print any one of them. If no solution, print "-1" in one line.

The first line contains one positive integer $T$ ($1\le T \le 1001$), denoting the number of test cases. For each test case:

Input one line containing one integer $S\,(0\le S \le 1000)$.

For each test case:

If no solution, print "-1" in one line.

If any solution exists, print two integers $r, c\,(1\le r,c \le 25)$ in the first line, denoting the size of the mine-sweeper map. Following $r$ lines each contains a string only containing "." or "X" of length $c$ where ".", "X" denote non-mine cells and mine cells respectively, denoting each row of the mine-sweeper map you construct.

Please notice that you needn't print the numbers on non-mine cells since these numbers can be determined by the output mine-sweeper map.

2
7
128

2 4
X..X
X...
5 19
.XXXX..XXXXX..XXXX.
XX.......X....X..XX
X........X....XXXX.
XX.....X.X....X..XX
.XXXX...XX....XXXX.

For the first test case, the map with numbers is as follows:

X21X
X211

The sum of these numbers equals 2+1+2+1+1=7.

2020 Multi-University Training Contest 10