Scrooge McDuck owns a circular island of radius R centered at the origin.
He wants to build a square tower there to keep all his wealth.
The wealth is quite huge, so the square of the foundation should be inscribed in the circle of the island. After reading a lot of popular magazines, Mrs. Beakley claimed
that according to feng shui, the entrance to the tower should be situated at the point (x_{1}, y_{1}), and the exit should be at the point (x_{2}, y_{2}). Of course, entrance and exit points should lie on the border of tower's foundation. Scrooge told you all these numbers and wants to know if it is possible to satisfy Mrs. Beakley's requirements.
Input
The first line contains an integer T — the number of test cases (1 ≤ T ≤ 1000). Each of the next T lines contains five integers separated by spaces: R, x_{1}, y_{1}, x_{2}, y_{2}.
1 ≤ R ≤ 10000. Points (x_{1}, y_{1}) and (x_{2}, y_{2}) are situated inside the circle.
Output
For each of the T cases output “YES” if the tower can be built,
and “NO” otherwise.
Sample
input  output 

3
2 1 1 1 1
2 1 1 0 0
1 1 0 1 0
 YES
NO
YES

Problem Author: folklore
Problem Source: Ural SU Contest. Petrozavodsk Summer Session, August 2008