IX Olimpiada Informatyczna 2001/2002

Task: min

Author: Piotr Chrz±stowskiWachtel, Wojciech Guzicki

III stage contest 
The operation of subtraction is not associative, e.g. (52)1=2, but 5(21)=4, therefore (52)1<>5(21). It implies that the value of the expression of the form 521 depends on the order of performing subtractions. In lack of brackets we assume that the operations are performed from left to right, i.e. the expression 521 denotes (52)1. We are given an expression of the form
x_{1} +/ x_{2} +/ ... +/ x_{n},
where each +/ denotes either + (plus) or  (minus), and x_{1},x_{2},...,x_{n} denote (pairwise) distinct variables. In an expression of the form
x_{1}x_{2}...x_{n}
we want to insert brackets in such a way as to obtain an expression equivalent to the given one. For example, if we want to obtain an expression equivalent to the expression
x_{1}x_{2}x_{3}+x_{4}+x_{5}x_{6}+x_{7}
we may insert brackets into
x_{1}x_{2}x_{3}x_{4}x_{5}x_{6}x_{7}
as follows:
((x_{1}x_{2})(x_{3}x_{4}x_{5}))(x_{6}x_{7}).
Note: Brackets that surround none or only one variable are not allowed.
7   + +  +a correct answer is in the following output file min.out:
(()())()