C. Bring Balancetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputAlina has a bracket sequence s of length 2n, consisting of n opening brackets '(' and n closing brackets ')'. As she likes balance, she wants to turn this bracket sequence into a balanced bracket sequence.In one operation, she can reverse any substring of s.What's the smallest number of operations that she needs to turn s into a balanced bracket sequence? It can be shown that it's always possible in at most n operations.As a reminder, a sequence of brackets is called balanced if one can turn it into a valid math expression by adding characters + and 1. For example, sequences (())(), (), and (()(())) are balanced, while )(, ((), and (()))( are not.InputThe first line of the input contains a single integer t (1 \le t \le 2 \cdot 10^4)  — the number of test cases. The description of the test cases follows.The first line of each test case contains a single integer n (1 \le n \le 10^5).The second line of each test case contains a string s of length 2n, consisting of n opening and n closing brackets.The sum of n over all test cases doesn't exceed 2\cdot 10^5.OutputFor each test case, in the first line output a single integer k (0 \le k \le n)  — the smallest number of operations required.The i-th of the next k lines should contain two integers l_i, r_i (1 \le l_i \le r_i \le 2n), indicating that in the i-th operation, Alina will reverse the substring s_ls_{l+1} \ldots s_{r-1}s_r. Here the numeration starts from 1.If there are multiple sequences of operations with the smallest length which transform the sequence into a balanced one, you can output any of them.ExampleInput
32(())5())((()))(6())((()))(()Output
0
2
3 4
9 10
1
2 11NoteIn the first test case, the string is already balanced.In the second test case, the string will be transformed as follows: ())((()))( \to ()()(()))( \to ()()(())(), where the last string is balanced.In the third test case, the string will be transformed to ((()))((())), which is balanced.
32(())5())((()))(6())((()))(()
0 2 3 4 9 10 1 2 11
['brute force', 'constructive algorithms', 'greedy', '*2600']