D. Bracket Coloringtime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputA 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:  the bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)");  the bracket sequences ")(", "(" and ")" are not. A bracket sequence is called beautiful if one of the following conditions is satisfied:  it is a regular bracket sequence;  if the order of the characters in this sequence is reversed, it becomes a regular bracket sequence. For example, the bracket sequences "()()", "(())", ")))(((", "))()((" are beautiful.You are given a bracket sequence s. You have to color it in such a way that:  every bracket is colored into one color;  for every color, there is at least one bracket colored into that color;  for every color, if you write down the sequence of brackets having that color in the order they appear, you will get a beautiful bracket sequence. Color the given bracket sequence s into the minimum number of colors according to these constraints, or report that it is impossible.InputThe 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.OutputFor each test case, print the answer as follows:  if it is impossible to color the brackets according to the problem statement, print -1;  otherwise, print two lines. In the first line, print one integer k (1 \le k \le n) — the minimum number of colors. In the second line, print n integers c_1, c_2, \dots, c_n (1 \le c_i \le k), where c_i is the color of the i-th bracket. If there are multiple answers, print any of them. ExampleInput
48((())))(4(())4))((3(()Output
2
2 2 2 1 2 2 2 1
1
1 1 1 1
1
1 1 1 1
-1

48((())))(4(())4))((3(()
2 2 2 2 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 -1 
['constructive algorithms', 'greedy', '*1400']