Counting Pairs with Limited Difference

You are given an array of N integers and an integer k. Your task is to count the number of pairs \((i,j)\) such that \(i < j\) and the absolute difference between A_i and A_j is at most \(k\), i.e.,

[ |A_i - A_j| \le k ]

The array may be unsorted, and the straightforward approach of examining every pair would be too slow for large inputs. A more optimal approach involves sorting the array and then using a two-pointer technique to efficiently count all valid pairs.

inputFormat

The input is given from stdin and consists of three lines:

1. The first line contains an integer \(N\) representing the number of elements in the array.
2. The second line contains \(N\) space-separated integers representing the elements of the array.
3. The third line contains an integer \(k\) representing the maximum allowed difference.

outputFormat

Output a single integer to stdout which is the number of pairs \((i,j)\) that satisfy the condition \(|A_i - A_j| \le k\).

## sample

3
1 3 5
2

2

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