Solve the programming task below in a Python markdown code block.
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You are given a convex polygon with N vertices.

You have to find any ⌊N/10⌋ distinct points with integer coordinates that lie strictly inside the polygon, or determine that such a set of points doesn't exist.

Note: ⌊⌋ denotes the floor function, typically used in integer division.

------ Input ------ 

The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
The first line of each test case contains a single integer N denoting the number of vertices of the polygon.
The following N lines describe the vertices of the polygon in anticlockwise order. Each of these lines contains two space-separated integers x and y denoting the coordinates of one vertex.

------ Output ------ 

For each test case, if a valid set of points doesn't exist, print a single line containing the integer -1. Otherwise, print ⌊N/10⌋ lines. Each of these lines should contain two space-separated integers denoting the coordinates of one point.

The coordinates of all points should be integers with absolute value not exceeding 10^{9}. If there are multiple solutions, you may print any one.

------ Constraints ------ 

$1 ≤ T ≤ 10^{5}$
$10 ≤ N ≤ 10^{5}$
$sum of N over all test cases ≤ 5 · 10^{5}$
$|x|, |y| ≤ 10^{9}$
$no three vertices of the polygon will be collinear$

------ Subtasks ------ 

Subtask #1 (30 points): 1 ≤ T ≤ 100, 10 ≤
N ≤ 100

Subtask #2 (70 points): original constraints

------ Example ------ 

------ Input Format ------ 

1
11
0 0
1 1
2 3
2 5
0 10
-2 10
-5 9
-8 7
-8 4
-6 1
-2 0

------ Output Format ------ 

0 1

------ Explanation ------ 

Example case 1: The polygon is shown in the picture:

You are required to output exactly ⌊N/10⌋ = ⌊11/10⌋ = 1 point.

One possible point that you can output is (0, 1). You can also output (0, 2), (-1, 3) or (1, 3).

However, (0, 0) is a wrong answer, because this point lies on the border of the convex polygon.

If you output (-1, -1), that's also a wrong answer, because this point lies outside the convex polygon. You can't output (1.1, 1.5) either, because it doesn't have integer coordinates, though it lies strictly inside the polygon.