| 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. | |
| ### Input | |
| 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. | |
| ### Output | |
| 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. | |