CF1732B Ugu

A binary string is a string consisting only of the characters 0 and 1. You are given a binary string $ s_1 s_2 \ldots s_n $ . It is necessary to make this string non-decreasing in the least number of operations. In other words, each character should be not less than the previous. In one operation, you can do the following: - Select an arbitrary index $ 1 \leq i \leq n $ in the string; - For all $ j \geq i $ , change the value in the $ j $ -th position to the opposite, that is, if $ s_j = 1 $ , then make $ s_j = 0 $ , and vice versa. What is the minimum number of operations needed to make the string non-decreasing?

Each test consists of multiple test cases. The first line contains an integer $ t $ ( $ 1 \leq t \leq 10^4 $ ) — the number of test cases. The description of test cases follows. The first line of each test cases a single integer $ n $ ( $ 1 \leq n \leq 10^5 $ ) — the length of the string. The second line of each test case contains a binary string $ s $ of length $ n $ . It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, output a single integer — the minimum number of operations that are needed to make the string non-decreasing.

In the first test case, the string is already non-decreasing. In the second test case, you can select $ i = 1 $ and then $ s = \mathtt{01} $ . In the third test case, you can select $ i = 1 $ and get $ s = \mathtt{010} $ , and then select $ i = 2 $ . As a result, we get $ s = \mathtt{001} $ , that is, a non-decreasing string. In the sixth test case, you can select $ i = 5 $ at the first iteration and get $ s = \mathtt{100001} $ . Then choose $ i = 2 $ , then $ s = \mathtt{111110} $ . Then we select $ i = 1 $ , getting the non-decreasing string $ s = \mathtt{000001} $ .