Hansel and Grethel

Time Limit: 2 Seconds
Memory Limit: 65536 KB

On a warm summer afternoon, Hansel and Grethel are walking together in the
fields. It is getting late and, to be honest, they are lost. Grethel is a little
scared, still vividly remembering the last time they got lost in the forest.
That time, an evil witch had locked them inside a house built of gingerbread
and sugar! But Hansel can reassure her: this time they are well prepared. Hansel
has taken a map and a compass with him!

Hansel picks two clearly outstanding features in the landscape, and uses the
compass to measure the direction towards both objects. Grethel locates the objects
on the map, and writes down the corresponding map coordinates. Based on this
information, they will be able to accurately determine their own position on
the map.

The coordinates of two marker objects, and the direction (angle from the North)
towards these objects are known. Write a program which uses this data to calculate
the coordinates of Hansel and Grethel's current location.

**Input**

The first line of the input contains one positive number: the number of situations
in which a position must be determined. Following are two lines per situation,
describing the two marker objects. Each marker object is described by a line
containing three integer numbers:

> the x-coordinate of the object on the map (0 <= x <= 100);

the x-axis runs West-to-East on the map, with increasing values towards the
East.

> the y-coordinate of the object on the map (0 <= y <= 100);

the y-axis runs South-to-North on the map, with increasing values towards the
North.

> the direction d of the object in degrees (0 <= d < 360);

with 0 = North, 90 = East, 180 = South, and so on.

To keep the position calculations accurate, Hansel makes sure that the directions
of the two objects are not exactly equal, and do not differ by exactly 180.

**Output**

One line per situation, containing the result of the position calculation: two
numbers, separated by a space, each having exactly 4 digits after the decimal
point. These numbers represent the x and y coordinates of the position of Hansel
and Grethel (0 <= x, y <= 100). Round the numbers as usual: up if the
next digit would be >= 5, down otherwise.

**Sample Input**

2

30 50 90

20 40 180

30 40 96

20 20 150

**Sample Output**

20.0000 50.0000

7.0610 42.4110

Source:

**Northwestern Europe 2002**
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