Solve the programming task below in a Python markdown code block.
Watson gives a circle and a triangle in a 2-dimensional plane to Sherlock. Sherlock has to tell if they intersect/touch each other. 

The circle is centered at $(x_c,y_c)$ and has radius $\mbox{R}$.   

Input Format 

The first line contains $\mathbf{T}$, the number of test cases. 

Each test case consists of $x_c$, $\boldsymbol{y}_{c}$ and $\mbox{R}$ in one line. 

The next three lines each contains $x_i,y_i$ denoting the vertices of the triangle.   

Output Format 

For each test case, print YES if the triangle touches or intersects the circle; otherwise, print NO.   

Constraints 

$1\leq T\leq30000$ 

$1\leq R\leq2000$ 

$-2000\leq x_c,y_c\leq2000$ 

$-5000\leq x_i,y_i\leq5000$ 

Note: There will be no degenerate triangles (i.e. triangles with area 0)  

Sample Input  

2
0 0 10
10 0
15 0
15 5
0 0 10
0 0
5 0
5 5

Sample Output    

YES
NO

Explanation 

In the first case, the triangle is touching the circle. In the second case, it neither touches nor intersects the circle.