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Maximize Subarrays After Removing One Conflicting Pair

You are given an integer n which represents an array nums containing the numbers from 1 to n in order.

You are given an integer n which represents an array nums containing the numbers from 1 to n in order. Additionally, you are given a 2D array conflictingPairs, where conflictingPairs[i] = [a, b] indicates that a and b form a conflicting pair.

Remove exactly one element from conflictingPairs. Afterward, count the number of non-empty subarrays of nums which do not contain both a and b for any remaining conflicting pair [a, b].

Return the maximum number of subarrays possible after removing exactly one conflicting pair.

Example 1

Input: n = 4, conflictingPairs = [[2,3],[1,4]]

Output: 9

Example 2

Input: n = 5, conflictingPairs = [[1,2],[2,5],[3,5]]

Output: 12

Constraints

  • 2 <= n <= 10^5
  • 1 <= conflictingPairs.length <= 2 * n
  • conflictingPairs[i].length == 2
  • 1 <= conflictingPairs[i][j] <= n
  • conflictingPairs[i][0] != conflictingPairs[i][1]

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