B'This is the hard version of the problem. The only difference between the two versions is that the harder version asks additionally for a minimum number of subsegments. Tokitsukaze has a binary string s of length n , consisting only of zeros and ones, n is even. Now Tokitsukaze divides s into the minimum number of contiguous subsegments, and for each subsegment, all bits in each subsegment are the same. After that, s is considered good if the lengths of all subsegments are even. For example, if s is "11001111", it will be divided into "11", "00" and "1111". Their lengths are 2 , 2 , 4 respectively, which are all even numbers, so "11001111" is good. Another example, if s is "1110011000", it will be divided into "111", "00", "11" and "000", and their lengths are 3 , 2 , 2 , 3 . Obviously, "1110011000" is not good. Tokitsukaze wants to make s good by changing the values of some positions in s . Specifically, she can perform the operation any number of times: change the value of s_i to '0 ' or '1 ' ( 1 <= q i <= q n ). Can you tell her the minimum number of operations to make s good? Meanwhile, she also wants to know the minimum number of subsegments that s can be divided into among all solutions with the minimum number of operations. The first contains a single positive integer t ( 1 <= q t <= q 10 ,000 ) -- the number of test cases. For each test case, the first line contains a single integer n ( 2 <= q n <= q 2 cdot 10^5 ) -- the length of s , it is guaranteed that n is even. The second line contains a binary string s of length n , consisting only of zeros and ones. It is guaranteed that the sum of n over all test cases does not exceed 2 cdot 10^5 . For each test case, print a single line with two integers -- the minimum number of operations to make s good, and the minimum number of sub'...