IX Olimpiada Informatyczna 2001/2002

Task: min
Author: Piotr Chrz±stowski-Wachtel, Wojciech Guzicki

III stage contest  

The operation of subtraction is not associative, e.g. (5-2)-1=2, but 5-(2-1)=4, therefore (5-2)-1<>5-(2-1). It implies that the value of the expression of the form 5-2-1 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 5-2-1 denotes (5-2)-1. We are given an expression of the form

x1 +/- x2 +/- ... +/- xn,

where each +/- denotes either + (plus) or - (minus), and x1,x2,...,xn denote (pairwise) distinct variables. In an expression of the form


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


we may insert brackets into


as follows:


Note: Brackets that surround none or only one variable are not allowed.


Write a program which:


In the first line of the text file min.in there is one integer n, 2<=n<=1 000 000. This is the number of variables in the given expression. In each of the following n-1 lines there is one character + or -. In the i-th line there is the sign appearing between xi-1 and xi in the given expression.


In the first line of the output text file min.out your program should write the requested way of bracket insertion into the expression x1-x2-...-xn. Only brackets and minuses (without spaces between them) should be written, and the variables x1,x2,...,xn ought to be skipped. You may assume that for the test data there is always a solution. If there exist many possible solutions your program should write one of them.


For the following input file min.in:
a correct answer is in the following output file min.out: