Given a 0-indexed integer array nums of size n and two integers lower and upper, return the number of fair pairs.

A pair (i, j) is fair if:

• 0 <= i < j < n, and
• lower <= nums[i] + nums[j] <= upper

 

Example 1:

Input: nums = [0,1,7,4,4,5], lower = 3, upper = 6
Output: 6
Explanation: There are 6 fair pairs: (0,3), (0,4), (0,5), (1,3), (1,4), and (1,5).

Example 2:

Input: nums = [1,7,9,2,5], lower = 11, upper = 11
Output: 1
Explanation: There is a single fair pair: (2,3).

 

Constraints:

• 1 <= nums.length <= 105
• nums.length == n
• -109 <= nums[i] <= 109
• -109 <= lower <= upper <= 109