#P1761. TheMummyReturns

TheMummyReturns

The mummy returns! Imhotep has caught O’Connell’slittle child to the Oasis of Ahm Shere to resurrect the Scorpion King. Torescue their son, O’Connell and Evelyn follow him, as well as our famousplayboy, Jonathan. The Scorpion King gobbles up the power of Imhotep andbecomes more powerful. The only way to kill him is to stab him with the Swordof Holy, which is in the hand of our playboy. This was simple because Jonathanwas good at playing dart. But things turn bad when Imhotep is between Jonathanand the Scorpion King. If the sword stabs Imhotep before the Scorpion King,Imhotep will get back his power and become unbeatable! The two heroes, O’Connelland Evelyn, are fighting to make the two devil unmoved, and the playboy,Jonathan, is trying to kill the Scorpion King without hurting Imhotep. Will hemake it?

To simplify theproblem, we assume that the two devils are two untouched circles, the sword isa point outside the circles, and its flying path is a straight ray. Giving thedescription of the two circles and the point, can you tell if there is a rayfrom the point which can intersect the circle of the Scorpion King withoutintersect the circle of Imhotep? Here two items intersect means they share atleast one common point.


Input

The input file consists of multiple test cases.
The only one line of each test case consists following parameters: Xs, Ys, Xi, Yi, Ri, Xk, Yk, Rk.
(Xs, Ys) is the location of the Sword of Holy.
(Xi, Yi) is the location of Imhotep, and Ri is its radius.
(Xk, Yk) is the location of the Scorpion King, and Rk is its radius.
Your program should process to the end of the input file.

Output

For each test case, output one line consisting of one English word “Yes” if Jonathon can kill the Scorpion King without hurt Imhotep, or “No” if not.

Sample Input

0 0 0 1 0.5 0 3 0.5
0 0 0 1 0.5 1 0 0.5

Sample Output

</p>
No
Yes

HINT

Source