L. Circles
time limit per test
5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Geo Ghaffar has become the boss and he didn't want to tell Da7doo7 "You're FIRED" so he told him "solve this problem or you're FIRED", knowing that Da7doo7 is bad at geometry. Of course Da7doo7 called you, his best friend, for help.

You are given $$$n$$$ distinct points in a $$$2D$$$ plane with integer coordinates. You will draw a finite circle in such a way it passes through the maximum number of points. Since you hate floating numbers, you only have to print this maximum number.

The above picture illustrates the first example. The green circle is the optimal choice to achieve the maximum number as it passes through all $$$4$$$ points, whereas the blue circle only passes through $$$2$$$ points.
Input

The first line of the input contains a single integer $$$T$$$ ($$$1 \le T \le 100$$$) representing the number of test cases.

For each test case, the first line contains a single integer $$$n$$$ ($$$2 \le n \le 200$$$) denoting the number of points. Each of the next $$$n$$$ lines contain two integers $$$x_i$$$ and $$$y_i$$$ ($$$-10^6 \le x_i, y_i \le 10^6$$$) — the coordinates of every point. It is guaranteed that the given points are distinct.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$200$$$.

Output

For each test case, print the answer in a single line.

Examples
Input
1
4
0 1
1 0
0 0
1 1
Output
4
Input
1
30
-54 -27
-74 91
-74 33
-45 -73
15 20
-35 66
-27 -85
53 24
-79 -62
40 29
16 27
95 -79
60 63
-32 -44
-31 -69
100 1
-91 -59
80 -18
77 -5
-38 64
-68 -67
-94 97
31 -41
-39 97
42 40
6 -19
-92 -28
-80 -1
-21 11
-90 -45
Output
3