Rectangle and Circle

Problem Description

Given a rectangle and a circle in the coordinate system(two edges of the rectangle are parallel with the X-axis, and the other two are parallel with the Y-axis), you have to tell if their borders intersect.

Note: we call them intersect even if they are just tangent. The circle is located by its centre and radius, and the rectangle is located by one of its diagonal.

Input

The first line of input is a positive integer P which indicates the number of test cases. Then P test cases follow. Each test cases consists of seven real numbers, they are X,Y,R,X1,Y1,X2,Y2. That means the centre of a circle is (X,Y)
and the radius of the circle is R, and one of the rectangle's diagonal is (X1,Y1)-(X2,Y2).

Output

For each test case, if the rectangle and the circle intersects, just output "YES" in a single line, or you should output "NO" in a single line.

Sample Input

2
1 1 1 1 2 4 3
1 1 1 1 3 4 4.5

Sample Output

YES
NO

Source

杭州电子科技大学第三届程序设计大赛

分析：圆与矩形有交点的充分必要条件是：点到四个线段的最短距离dmin<=radius && 点到四个线段的最长距离dmax>=radius。