Equal Angles

Time limit1sMemory limit128 MB

Summary

For each triangle, compute the two Brocard points, where the angle a point makes with each side in cyclic order stays equal.

Level: Medium7 of 10
Topics: Geometry, Math, Implementation
Solved: No attempts yet

Problem

The All-Equal company places towers on triangular plots so that the angles formed between a tower and the sides of its plot are all equal. For a triangle with vertices A, B, and C there are two such tower positions, call them P and Q:

P is the point with $\angle PAB = \angle PBC = \angle PCA$ .
Q is the point with $\angle QBA = \angle QCB = \angle QAC$ .

Given the triangle, find P and Q.

Input

The input contains several test cases. Each test case is a single line of six integers:

AX AY BX BY CX CY

Each integer is in the range $-100$ to $100$ . They give the three vertices of the triangle: $(AX, AY)$ , $(BX, BY)$ , and $(CX, CY)$ . The points are guaranteed to form a triangle: they are distinct and not all collinear. The input ends with a line of six 0s.

Output

For each test case, output four space-separated real numbers:

PX PY QX QY

where $(PX, PY)$ and $(QX, QY)$ are the two requested points. Print each real number with exactly two decimal places (rounded), separated by single spaces. Print no blank lines between outputs.

Examples1

Example 1

Input

-4 5 -10 0 7 0
-15 -5 15 -5 0 21
0 0 0 0 0 0

Expected output

-6.26 1.28 -1.96 3.07
0.01 3.66 -0.01 3.66