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Count Number of Bad Pairs

You are given a 0-indexed integer array nums.

You are given a 0-indexed integer array nums. A pair of indices (i, j) is a bad pair if i < j and j - i != nums[j] - nums[i].

Return the total number of bad pairs in nums.

Count Number of Bad Pairs diagram

Example 1

Input: nums = [4,1,3,3]

Output: 5

Explanation: The pair (0, 1) is a bad pair since 1 - 0 != 1 - 4. The pair (0, 2) is a bad pair since 2 - 0 != 3 - 4, 2 != -1. The pair (0, 3) is a bad pair since 3 - 0 != 3 - 4, 3 != -1. The pair (1, 2) is a bad pair since 2 - 1 != 3 - 1, 1 != 2. The pair (2, 3) is a bad pair since 3 - 2 != 3 - 3, 1 != 0. There are a total of 5 bad pairs, so we return 5.

Example 2

Input: nums = [1,2,3,4,5]

Output: 0

Explanation: There are no bad pairs.

Constraints

  • 1 <= nums.length <= 10^5
  • 1 <= nums[i] <= 10^9

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