Given $N$ points in a 2D plane and a nonnegative integer $D$, find the minimum number of points to remove so that there exists a line $f(x)=ax+b$ whose maximum absolute residual $\max |y_i - f(x_i)|$ on the remaining points does not exceed $D$.

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 $i$.

• $1 \leq T \leq 10^3$
• $1 \leq N \leq 5 \times 10^3$