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Find the Number of Copy Arrays

You are given an array original of length n and a 2D array bounds of length n x 2, where bounds[i] = [ui, vi].

You are given an array original of length n and a 2D array bounds of length n x 2, where bounds[i] = [ui, vi].

You need to find the number of possible arrays copy of length n such that:

Return the number of such arrays.

Example 1

Input: original = [1,2,3,4], bounds = [[1,2],[2,3],[3,4],[4,5]]

Output: 2

Explanation: The possible arrays are:

Example 2

Input: original = [1,2,3,4], bounds = [[1,10],[2,9],[3,8],[4,7]]

Output: 4

Explanation: The possible arrays are:

Example 3

Input: original = [1,2,1,2], bounds = [[1,1],[2,3],[3,3],[2,3]]

Output: 0

Explanation: No array is possible.

Constraints

  • 2 <= n == original.length <= 10^5
  • 1 <= original[i] <= 10^9
  • bounds.length == n
  • bounds[i].length == 2
  • 1 <= bounds[i][0] <= bounds[i][1] <= 10^9

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