write a go solution for F. Prefix Maximum Invariancetime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputGiven 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, operatornamemax(x_1,x_2,ldots,x_i)=operatornamemax(z_1,z_2,ldots,z_i) should hold for all 1<=i<=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^nsum_r=l^nf([a_l,a_l+1,ldots,a_r],[b_l,b_l+1,ldots,b_r]).InputEach test contains multiple test cases. The first line contains the number of test cases t (1<=t<=10^4). The description of the test cases follows. The first line of each test case contains an integer n (1<=n<=2*10^5).The second line contains n integers a_1,a_2,ldots,a_n (1<=a_i<=2*n).The third line contains n integers b_1,b_2,ldots,b_n (1<=b_i<=2*n).It is guaranteed that the sum of n over all test cases does not exceed 2*10^5.OutputFor 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).ExampleInput635 3 14 2 151 2 3 4 51 2 3 4 567 1 12 10 5 89 2 4 3 6 511265 1 2 6 3 43 1 6 5 2 422 21 1Output5
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NoteIn 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].. Output only the code with no comments, explanation, or additional text.