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:
(copy[i] - copy[i - 1]) == (original[i] - original[i - 1]) for 1 <= i <= n - 1.ui <= copy[i] <= vi for 0 <= i <= n - 1.Return the number of such arrays.
\n\n\n
Example 1:
\n\nInput: original = [1,2,3,4], bounds = [[1,2],[2,3],[3,4],[4,5]]
\n\nOutput: 2
\n\nExplanation:
\n\nThe possible arrays are:
\n\n[1, 2, 3, 4][2, 3, 4, 5]Example 2:
\n\nInput: original = [1,2,3,4], bounds = [[1,10],[2,9],[3,8],[4,7]]
\n\nOutput: 4
\n\nExplanation:
\n\nThe possible arrays are:
\n\n[1, 2, 3, 4][2, 3, 4, 5][3, 4, 5, 6][4, 5, 6, 7]Example 3:
\n\nInput: original = [1,2,1,2], bounds = [[1,1],[2,3],[3,3],[2,3]]
\n\nOutput: 0
\n\nExplanation:
\n\nNo array is possible.
\n\n
Constraints:
\n\n2 <= n == original.length <= 1051 <= original[i] <= 109bounds.length == nbounds[i].length == 21 <= bounds[i][0] <= bounds[i][1] <= 109给你一个长度为 n 的数组 original 和一个长度为 n x 2 的二维数组 bounds，其中 bounds[i] = [ui, vi]。
你需要找到长度为 n 且满足以下条件的 可能的 数组 copy 的数量：
1 <= i <= n - 1 ，都有 (copy[i] - copy[i - 1]) == (original[i] - original[i - 1]) 。0 <= i <= n - 1 ，都有 ui <= copy[i] <= vi 。返回满足这些条件的数组数目。
\n\n\n\n
示例 1
\n\n输入：original = [1,2,3,4], bounds = [[1,2],[2,3],[3,4],[4,5]]
\n\n输出：2
\n\n解释：
\n\n可能的数组为：
\n\n[1, 2, 3, 4][2, 3, 4, 5]示例 2
\n\n输入：original = [1,2,3,4], bounds = [[1,10],[2,9],[3,8],[4,7]]
\n\n输出：4
\n\n解释：
\n\n可能的数组为：
\n\n[1, 2, 3, 4][2, 3, 4, 5][3, 4, 5, 6][4, 5, 6, 7]示例 3
\n\n输入：original = [1,2,1,2], bounds = [[1,1],[2,3],[3,3],[2,3]]
\n\n输出：0
\n\n解释：
\n\n没有可行的数组。
\n\n\n
提示：
\n\n2 <= n == original.length <= 1051 <= original[i] <= 109bounds.length == nbounds[i].length == 21 <= bounds[i][0] <= bounds[i][1] <= 109copy[0] uniquely determines all other values.",
"Possible values for copy[0] are in [u[0], v[0]].",
"From left to right, compute valid ranges for each index by intersecting bounds with the previous range.",
"The answer is the size of the valid range for the last index."
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