For this problem, a possible median is defined as: The median value of a set containing an odd number of values. -or- One of all the integers between, but not including, the two median values of a set containing an even number of values.
Examples: 3 is the only possible median of the set (1, 5, 3, 2, 4). 2, 3 and 4 are all of the possible median values for the set (5, 1). There
are no possible median values for the set (1, 2, 3, 4), since there are no integers between 2 and 3.
You are given an array A of N unique nonnegative integers, all of which are < N (i.e. a permutation of the numbers 0...N-1), where 3 ≤ N ≤ 200,000. You are also given a length L (1 ≤ L ≤ N). Additionally, you are given Q (1 ≤ Q ≤ 200,000) queries, each containing a number x (0 ≤ x < N) and two indices i and j (0 ≤ i < j ≤ N).
Each query returns TRUE if and only if there exists at least one subrange, of at least L elements, of the range A[i]...A[j-1] (where the array indices start at 0), with x as a possible median. In other words, the answer is TRUE precisely when there exist a, b with i ≤ a < b < j with b - a ≥ L - 1 and with A[a]...A[b] having x as a possible median.
You wish to determine the number of queries which will return TRUE.
The first line contains a positive integer T (1 ≤ T ≤ 20), the number of test cases. T test cases follow.
The first line of each test case consists of a single integer, N. The next line consists of N space-separated integers, the A[i]. The line after that contains two space-separate d integers, L and Q.
Each of the remaining Q lines in the test case contains three space-separated integers, x, i and j.
These inputs are all integers, and will be input in decimal form, with no leading zeros, and no decimal points.
For each of the test cases numbered in order from 1 to T, output "Case #", followed by the case number, followed by ": ", followed by a single integer, the number of passing queries.
These outputs are all integers, and must be output in decimal form, with no leading zeros, and no decimal points.