Problem 3503 --Mine Sweeper

3503: Mine Sweeper

正确率: $0.00\%$ 下一题

Time Limit	$1$ 秒/Second(s)	Memory Limit	$512$ 兆字节/Megabyte(s)
提交总数	$11$	正确数量	$0$
裁判形式	标准裁判/Standard Judge	我的状态	尚未尝试
难度		分类标签

Description

A mine-sweeper map can be expressed as an r×cgrid, 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 16×30mine-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,cboth 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.

Input

The first line contains one positive integer

1≤T≤1001), denoting the number of test cases. For each test case:
Input one line containing one integer

S(0≤S≤1000).

Output

For each test case:
If no solution, print "-1" in one line.
If any solution exists, print two integers

r,c(1≤r,c≤25)in the first line, denoting the size of the mine-sweeper map. Following

rlines each contains a string only containing "." or "X" of length

cwhere ".", "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.

Sample Input复制

2
7
128

Sample Output复制

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.

提示


	
	
		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.

赛题来源/所属竞赛 2020 Multi-University Training Contest 10 N/A

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第一挑战	梦尘	694388	2020-12-30 21:34:21