AT_arc224_b [ARC224B] Adjacent Tiles

Let us place $ N $ square tiles of the same size on a plane so that they do not overlap. Then, what is the maximum possible number of pairs of different tiles that **share one full side**? Here, a pair of different tiles $ (a,b) $ is said to share one full side if and only if some side of $ a $ and some side of $ b $ coincide completely. $ T $ test cases are given; solve each of them.

The input is given from Standard Input in the following format, where $ \mathrm{case}_i $ denotes the $ i $ -th test case: > $ T $ $ \mathrm{case}_1 $ $ \mathrm{case}_2 $ $ \vdots $ $ \mathrm{case}_T $ Each test case is given in the following format: > $ N $

Output $ T $ lines. The $ i $ -th line should contain the answer for the $ i $ -th test case.

### Sample Explanation 1 This input contains six test cases. The figure below shows an example of an optimal arrangement of tiles for $ N=1,2,3,4 $ . - For the first test case, $ N=1 $ . - There is no pair of different tiles sharing one full side. - For the second test case, $ N=2 $ . - The pair of tiles $ ({\rm a,b}) $ shares one full side. - For the third test case, $ N=3 $ . - The pairs of tiles $ ({\rm a,b}),({\rm b,c}) $ share one full side. - For the fourth test case, $ N=4 $ . - The pairs of tiles $ ({\rm a,b}),({\rm a,c}),({\rm b,d}),({\rm c,d}) $ share one full side.  ### Constraints - $ 1 \le T \le 2 \times 10^5 $ - $ 1 \le N \le 10^{18} $ - All input values are integers.