Planet Meteor  - 1 Point

It's like Armageddon! Duck and cover! Your job, as the hottest new NASA tech with a 7-figure salary, is to keep the the world informed of any danger from space. Each day tons of data pours in about foreign bodies in outer space and where they're headed. And in your spare time, you also look for the danger for other planets as well.

Although the world is in 3-Space, we can use 2-D projections to make accurate enough estimates of danger. So, you will be given the location and radius of a circle, and the location and velocity vector for a point-meteor. You have to tell us, will they collide?!?

Assume that the planet revolves in a circle around the origin (0, 0). However, assume that the velocity of the meteor is so blindingly fast, that it is as if the planet is stationary.

Input Format
// Planet information
<x location of circle> <y location of circle> <radius of circle>

// Point-Meteor information
<x location of meteor> <y location of meteor>
<x component of velocity> <y component of velocity>

A -1 will signal the end of one test.

A double -1 will be signal the end of the page.

Note: Data will be given as integers only.

The input file will be called jin03.txt.

Output Format
Your output should warn the people if they are in any danger:

If there is no danger of impact:
SAFE, the planet is in no danger.

If impact is imminent:
DANGER, there is a chance of impact!

Example
Input
0 2 1
-5 5
1 0
-1
-1

Output
SAFE, the planet is in no danger.