B"Alina 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. The first line of the input contains a single integer t ( 1 <= t <= 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 <= n <= 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 . For each test case, in the first line output a single integer k (0 <= k <= n) -- the smallest number of operations required. The i -th of the next k lines should contain two integers l_i, r_i ( 1 <= l_i <= r_i <= 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. In 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 w"...