CF1837D.Bracket Coloring
普及/提高-
通过率:0%
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题目描述
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:
- 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.
输入格式
The first line contains one integer t ( 1≤t≤104 ) — the number of test cases.
Each test case consists of two lines. The first line contains one integer n ( 2≤n≤2⋅105 ) — 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⋅105 .
输出格式
For 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≤k≤n ) — the minimum number of colors. In the second line, print n integers c1,c2,…,cn ( 1≤ci≤k ), where ci is the color of the i -th bracket. If there are multiple answers, print any of them.
输入输出样例
输入#1
4 8 ((())))( 4 (()) 4 ))(( 3 (()
输出#1
2 2 2 2 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 -1