Given $N$ points in a 2D plane, remove $K$ of them and find the line $f(x)=ax+b$ that minimizes the maximum absolute residual $\max |y_i - f(x_i)|$ on the remaining points. Output that minimum error. An answer is accepted if the absolute or relative error from the correct value is less than $10^{-6}$.

Input is given from standard input in the following format: $T$ $case_1$ $case_2$

Output $T$ lines. On the $i$-th line, output the answer to case $i$.

• $1 \leq T \leq 10^4$
• $1 \leq N \leq 10^5$