Problem:
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Cross Points of Circles

For given two circles $c1$ and $c2$, print the coordinates of the cross points of them.

Input

The input is given in the following format.

$c1x\; c1y\; c1r$

$c2x\; c2y\; c2r$

$c1x$, $c1y$ and $c1r$ represent the coordinate and radius of the first circle.
$c2x$, $c2y$ and $c2r$ represent the coordinate and radius of the second circle.
All input values are given in integers.

Output

Print the coordinates ($x1$, $y1$) and ($x2$, $y2$) of the cross points $p1$ and $p2$ respectively in the following rules.

If there is one cross point, print two coordinates with the same values.

Print the coordinate with smaller $x$ first. In case of a tie, print the coordinate with smaller $y$ first.

The output values should be in a decimal fraction with an error less than 0.000001.

Constraints

The given circle have at least one cross point and have different center coordinates.

$-10,000 \leq c1x, c1y, c2x, c2y \leq 10,000$

$1 \leq c1r, c2r \leq 10,000$

Sample Input and Output

Sample Input 1

0 0 2
2 0 2

Sample Output 1

1.00000000 -1.73205080 1.00000000 1.73205080

Sample Input 2

0 0 2
0 3 1

Sample Output 2

0.00000000 2.00000000 0.00000000 2.00000000

Solution in Ruby (judge verdict: Wrong Answer)

require 'matrix'

c1x, c1y, r1 = gets.split.map &:to_i
c2x, c2y, r2 = gets.split.map &:to_i

c1 = Vector[c1x, c1y]
c2 = Vector[c2x, c2y]

cos_t = (r1**2 + (c2-c1).norm**2 - r2**2) / (2 * r1 * (c2-c1).norm)
sin_t = (1 - cos_t**2) ** (1/2.0)
p1 = [c1x + r1*cos_t, c1y + r1*sin_t]
p2 = [c1x + r1*cos_t, c1y - r1*sin_t]

puts "%.7f %.7f %.7f %.7f" % [p1[0], p1[1], p2[0], p2[1]]