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 and has radius .

Input Format
The first line contains , the number of test cases.
Each test case consists of , and in one line.
The next three lines each contains 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




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.