A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters "1" and "+" between the original characters of the sequence. For example:
A bracket sequence is called beautiful if one of the following conditions is satisfied:
For example, the bracket sequences "()()", "(())", ")))(((", "))()((" are beautiful.
You are given a bracket sequence $$$s$$$. You have to color it in such a way that:
Color the given bracket sequence $$$s$$$ into the minimum number of colors according to these constraints, or report that it is impossible.
The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.
Each test case consists of two lines. The first line contains one integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) — the number of characters in $$$s$$$. The second line contains $$$s$$$ — a string of $$$n$$$ characters, where each character is either "(" or ")".
Additional constraint on the input: the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
For each test case, print the answer as follows:
48((())))(4(())4))((3(()
2 2 2 2 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 -1
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