Do you think that drawing polygons is easy? This is not the case when you have some restrictions. In this problem all you have to do is just to draw a polygon. It must have exactly \textbf{N }vertices. It must contain no self-intersections. No three consecutive vertices of the polygon must be collinear. All coordinates of its vertices must be integers between \textbf{0} and \textbf{10 000}, inclusive. Easy, right? There is one more small restriction though. The number of inner angles of this polygon equal to \textbf{90°} must be as large as possible under these constraints. What do you think about it now? \InputFile Contains the number of test cases \textbf{T} (\textbf{1} ≤ \textbf{T} ≤ \textbf{30}) followed by \textbf{T} integer numbers \textbf{N} (\textbf{3} ≤ \textbf{N} ≤ \textbf{1000}). \OutputFile For each test case print the maximum possible number of inner angles equal to \textbf{90°} followed by \textbf{N} pairs of integers -the coordinates of the vertices of the polygon in either clockwise or counterclockwise order. Of course, more than one solution is possible, so output any of them.