Mobile positioning is a technology used by telecommunication companies to approximate where a mobile phone is. Although it is not that accurate than some alternatives, such as GPS, it is quick and costs less. In this problem, we consider a special version of mobile positioning with two base stations used.
Mobile Positioning
The graph shows how mobile positioning works. P1(x1, y1) and P2(x2, y2) are two base stations communicating with mobile phones. Someone is walking from Point A to Point C in a straight line with constant speed. The positioning has 5 steps:
At Point A, his mobile phone emits a signal to base station P1.
After time t1, the base station P1 receives the signal and echoes back immediately.
After time t2, the mobile phone gets the signal from the base station P1 at Point B, and then transmits a new signal to the base station P2 immediately.
The signal transfers for time t3 and arrives at the base station P2, and then a new signal by P2 is sent back immediately.
After time t4, the mobile phone receives the signal at Point C.
It is well known that signals go off in all directions, like a series of circles that shares a same center. With the speed of signal v given, please find out the coordinates of ALL possible Point A.
Input
The input contains no more than 30 cases. Each case contains two lines. The first line is 4 numbers x1, y1, x2, y2 (-10000 < x1, y1, x2, y2 < 10000). The second line has 5 numbers, t1, t2, t3, t4, v (0 ≤ t1, t2, t3, t4 < 10000, 0 < v < 10000).
Proceed to the end of file.
Output
For each case, output a single line contains the number of possible Point A, then n lines of the coordinates in the form "x y" in ascending order. Keep two digits after the decimal point. If the number of possible Point A is infinite, simply output -1. You can assume that there is at least one possible Point A.
Sample Input
0 12 16 6
6 10 3 5 2
Sample Output
4
0.00 0.00
7.89 21.04
11.08 7.38
11.38 8.19
