A mine-sweeper map can be expressed as an r×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 16×30 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.
输入格式
The first line contains one positive integer T (1≤T≤1001), denoting the number of test cases. For each test case:
Input one line containing one integer S(0≤S≤1000).
输出格式
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 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.