Problem Description

Bob accidentally spilled some drops of ink on the paper. The initial position of the i-th drop of ink is $(x_i,y_i)$, which expands outward by $0.5$ centimeter per second, showing a circle.
The curious Bob wants to know how long it will take for all the inks to become connected. In order to facilitate the output, please output the square of the time.

Input

The first line of input contains one integer $T(1\leq T \leq5)$, indicating the number of test cases.
For each test case, the first line contains one integer $n(2\leq n \leq5000)$, indicating the number of ink on the paper.
Each of the next n lines contains $2$ integers $(x_i,y_i)$(|$x_i$|$\leq10^9$,|$y_i$|$\leq10^9$), indicating that x and y coordinates of the ink.

Output

For each test case, output one line containing one decimal, denoting the answer.

2
3
0 0
1 1
0 1
5
1 1
4 5
1 4
2 6
3 10

1
17