One day, you found an old scroll with strange texts on it.</p>

You revealed that the text was actually an expression denoting the position of treasure. The expression consists of following three operations:

• From two points, yield a line on which the points lie.
• From a point and a line, yield a point that is symmetric to the given point with respect to the line.
• From two lines, yield a point that is the intersection of the lines.

The syntax of the expression is denoted by following BNF:

<expression>      ::= <point>
<point>           ::= <point-factor> | <line> "@" <line-factor> | <line> "@" <point-factor> | <point> "@" <line-factor>
<point-factor>    ::= "(" <number> "," <number> ")" | "(" <point> ")"
<line>            ::= <line-factor> | <point> "@" <point-factor>
<line-factor>     ::= "(" <line> ")"
<number>          ::= <zero-digit> | <positive-number> | <negative-number>
<positive-number> ::= <nonzero-digit> | <positive-number> <digit>
<negative-number> ::= "-" <positive-number>
<digit>           ::= <zero-digit> | <nonzero-digit>
<zero-digit>      ::= "0"
<nonzero-digit>   ::= "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"

Each <point> or <point-factor> denotes a point, whereas each <line> or <line-factor> denotes a line. The former notion of <point-factor> (X,Y) represents a point which has X for x-coordinate and Y for y-coordinate on the 2-dimensional plane. "@" indicates the operations on two operands. Since each operation is distinguishable from others by its operands' types (i.e. a point or a line), all of these operations are denoted by the same character "@". Note that "@" is left-associative, as can be seen from the BNF.

Your task is to determine where the treasure is placed.

입력 형식

The input consists of multiple datasets. Each dataset is a single line which contains an expression denoting the position of treasure.</p>

It is guaranteed that each dataset satisfies the following conditions:

• The length of the string never exceeds 10².
• If both operands of "@" are points, their distance is greater than 1.
• If both operands of "@" are lines, they are never parallel.
• The absolute values of points' coordinates never exceed 10² at any point of evaluation.

You can also assume that there are at most 100 datasets.

The input ends with a line that contains only a single "#".

출력 형식

For each dataset, print the X and Y coordinates of the point, denoted by the expression, in this order.</p>

The output will be considered correct if its absolute or relative error is at most 10⁻².

예제 입력

((0,0)@(1,1))@((4,1)@(2,5))
((0,0)@(3,1))@((1,-3)@(2,-1))
(0,0)@(1,1)@(4,1)
(0,0)@((1,1)@(4,1))
(((0,0)@((10,20)@(((30,40))))))
((0,0)@(3,1))@((1,-3)@(2,-1))@(100,-100)@(100,100)
#

예제 출력

3.00000000 3.00000000
3.00000000 1.00000000
1.00000000 4.00000000
0.00000000 2.00000000
-10.00000000 10.00000000
-99.83681795 -91.92248853