Define performing a bubble on an array (b_1, b_2, \ldots, b_m) to be performing the following action: For each integer (i) ((1 \leq i \lt m)) in order , if (b_i \gt b_{i+1}), swap (b_i) and (b_{i+1}). For each integer (i) ((1 \leq i \lt m)) in reverse order , if (b_i \gt b_{i+1}), swap (b_i) and (b_{i+1}). For example, if we perform a bubble on (1, 1, 0), we would transform it as follows: (\color{red}{1, 1}, 0 \to 1, \color{red}{1, 0} \to 1, 0, 1). If we perform a reverse bubble on (1, 1, 0), we would transform it as follows: (1, \color{red}{1, 0} \to\color{red}{1, 0}, 1 \to 0, 1, 1). You are given an array (a_1, a_2, \ldots, a_n) consisting of only 0 s and 1 s and a binary string(^{\text{∗}}) (s) of length (n). You perform (n) operations in order , where the (i)-th operation performs a bubble on (a) if (s_i = 1) and performs a reverse bubble on (a) if (s_i = 0). For each of the (n + 1) states of (a) — before any operations have been performed and after each operation — count the number of inversions(^{\text{†}}) in (a). (^{\text{∗}})A binary string is a string that only contains 0 s and 1 s. (^{\text{†}})An inversion in an array (c) of length (m) is a pair of indices (i, j) such that (1 \leq i \lt j \leq m) and (c_i \gt c_j). The first line of each input contains (t) ((1 \leq t \leq 10^4)) — the number of test cases. The first line of each test case contains (n) ((1 \leq n \leq 5 \cdot 10^5)) — the length of (a) and (s). The second line of each test case contains (a_1, a_2, \ldots, a_n) ((0 \leq a_i \leq 1)) — the array (a). The third line of each test case contains (s) ((s_i \in \{0, 1\}), (|s| = n)(^{\text{∗}})) — the binary string (s). It is guaranteed that the sum of (n) over all test cases does not exceed $$$5 \cdot