So this is an old classic history about some guy trying to solve an incredible problem hidden behind the statement about competitive programming, but in this history Felmon(the guy) is trying to maximize the area of some rectangle with only a cord, yeah a cord, claps for this awesome statement.

Input

An integer T ($1 \leq T \le 10^4$) the test cases.

The next T lines have a number C ($1 \leq C \leq 10^5$), the length of the cord.

Output

T lines containing three integers X, Y and A, the length of the shortest side, the length of the longest side and the maximum area, respectively, rounded to three decimal digits.