You are given an integer array nums of length n where nums is a permutation of the integers in the range [1, n]. You are also given a 2D integer array sequences where sequences[i] is a subsequence of nums.

Check if nums is the shortest possible and the only supersequence. The shortest supersequence is a sequence with the shortest length and has all sequences[i] as subsequences. There could be multiple valid supersequences for the given array sequences.

For example, for sequences = [[1,2],[1,3]], there are two shortest supersequences, [1,2,3] and [1,3,2].
While for sequences = [[1,2],[1,3],[1,2,3]], the only shortest supersequence possible is [1,2,3]. [1,2,3,4] is a possible supersequence but not the shortest.

Return true if nums is the only shortest supersequence for sequences, or false otherwise.

A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.

Example 1:

Input: nums = [1,2,3], sequences = [[1,2],[1,3]]
Output: false
Explanation: There are two possible supersequences: [1,2,3] and [1,3,2].
The sequence [1,2] is a subsequence of both: [1,2,3] and [1,3,2].
The sequence [1,3] is a subsequence of both: [1,2,3] and [1,3,2].
Since nums is not the only shortest supersequence, we return false.

Example 2:

Input: nums = [1,2,3], sequences = [[1,2]]
Output: false
Explanation: The shortest possible supersequence is [1,2].
The sequence [1,2] is a subsequence of it: [1,2].
Since nums is not the shortest supersequence, we return false.

Example 3:

Input: nums = [1,2,3], sequences = [[1,2],[1,3],[2,3]]
Output: true
Explanation: The shortest possible supersequence is [1,2,3].
The sequence [1,2] is a subsequence of it: [1,2,3].
The sequence [1,3] is a subsequence of it: [1,2,3].
The sequence [2,3] is a subsequence of it: [1,2,3].
Since nums is the only shortest supersequence, we return true.

Constraints:

n == nums.length
1 <= n <= 10⁴
nums is a permutation of all the integers in the range [1, n].
1 <= sequences.length <= 10⁴
1 <= sequences[i].length <= 10⁴
1 <= sum(sequences[i].length) <= 10⁵
1 <= sequences[i][j] <= n
All the arrays of sequences are unique.
sequences[i] is a subsequence of nums.

Sequence Reconstruction

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