Given two arrays (x) and (y) both of size (m), let (z) be another array of size (m) such that the prefix maximum at each position of (z) is the same as the prefix maximum at each position of (x). Formally, (\operatorname{max}(x_1,x_2,\ldots,x_i)=\operatorname{max}(z_1,z_2,\ldots,z_i)) should hold for all (1 \leq i \leq m). Define (f(x,y)) to be the maximum number of positions where (z_i=y_i) over all possible arrays (z). You are given two sequences of integers (a) and (b), both of size (n). Please find the value of (\sum_{l=1}^n\sum_{r=l}^n f(a_l,a_{l+1},\ldots,a_r, b_l,b_{l+1},\ldots,b_r)). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains an integer (n) ((1 \leq n \leq 2\cdot 10^5)). The second line contains (n) integers (a_1,a_2,\ldots,a_n) ((1 \leq a_i \leq 2\cdot n)). The third line contains (n) integers (b_1,b_2,\ldots,b_n) ((1 \leq b_i \leq 2\cdot 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 the sum of (f(a_l,a_{l+1},\ldots,a_r, b_l,b_{l+1},\ldots,b_r)) over all pairs of ((l,r)). In the first test case, the answer is the sum of the following: (f(5,4)=0), using (z=5). (f(3,2)=0), using (z=3). (f(1,1)=1), using (z=1). (f(5,3,4,2)=1), using (z=5,2). (f(3,1, 2,1)=1), using (z=3,1). (f(5,3,1,4,2,1)=2), using (z=5,2,1).