Subtraction is not associative, e.g., $(5 - 2) - 1 = 2$, while $5 - (2 - 1) = 4$, and thus $(5 - 2) - 1 \neq 5 - (2 - 1)$. It follows that the value of an expression of the form $5 - 2 - 1$ depends on the order of subtractions. In the absence of parentheses, it is assumed that operations are performed from left to right, i.e., the expression $5 - 2 - 1$ means $(5 - 2) - 1$.

We are given an expression of the form $$x_1 \pm x_2 \pm \dots \pm x_n$$ where $\pm$ denotes either $+$ (plus) or $-$ (minus), and $x_1, x_2, \dots, x_n$ are distinct variables. We want to place parentheses in the expression of the form $$x_1 - x_2 - \dots - x_n$$ in such a way as to obtain an expression equivalent to the given one.

For example, to obtain an expression equivalent to $$x_1 - x_2 - x_3 + x_4 + x_5 - x_6 + x_7$$ we can place parentheses in $$x_1 - x_2 - x_3 - x_4 - x_5 - x_6 - x_7$$ for example, as follows: $$((x_1 - x_2) - (x_3 - x_4 - x_5)) - (x_6 - x_7)$$

Note: Parenthesizations where parentheses do not enclose any variable or enclose only a single variable are not allowed.

Task

Write a program that: reads the description of the given expression of the form $x_1 \pm x_2 \pm \dots \pm x_n$, determines how to insert parentheses into the expression $x_1 - x_2 - \dots - x_n$ to obtain an expression equivalent to the given one; you may insert at most $n - 1$ pairs of parentheses, * outputs this arrangement.

Input

The first line of standard input contains a single integer $n$, $2 \le n \le 1\,000\,000$. This is the number of variables in the given expression. Each of the next $n - 1$ lines contains a single character, $+$ or $-$. The $i$-th line contains the sign appearing in the given expression between $x_i$ and $x_{i+1}$.

Output

Your program should write to the first line of standard output the required way of inserting parentheses into the expression $x_1 - x_2 - \dots - x_n$. You must write only the parentheses and minus signs (without spaces between them), omitting the variables $x_1, x_2, \dots, x_n$. You may assume that a solution always exists for the test data. If there are multiple possible solutions, your program should output one of them.

Examples

Input 1

7
-
-
+
+
-
+

Output 1

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