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문제

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

    x1-x2-…-xn

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

    x1-x2-x3+x4+x5-x6+x7

we may insert brackets into

    x1-x2-x3-x4-x5-x6-x7

as follows:

    ((x1-x2)-(x3-x4-x5))-(x6-x7).

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

Write a program which:

  • reads from the standard input the description of the given expression of the form x1±x2±…±xn,
  • determines the way brackets may be inserted into the expression so as to obtain an expression x1-x2-…-xn equivalent to the given one; at most n-1 pairs of brackets may be inserted,
  • describes in the text file min.out this arrangement brackets.

입력

In the first line of the standard input 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.

 

출력

In the first line of the standard output 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.

예제 입력

7
-
-
+
+
-
+

예제 출력

((-)-(--))-(-)

힌트