Unique Quadruplets Sum

Given an array of integers and a target integer \(X\), find all unique quadruplets in the array that sum up to \(X\). Each quadruplet should be sorted in non-decreasing order and the list of all quadruplets should be sorted lexicographically.

Constraints:

• \(1 \leq n \leq 100\), where \(n\) is the number of elements in the array.
• \(-10^9 \leq arr[i] \leq 10^9\) for each \(arr[i]\) in the array.

Example 1:

Input:
6
1 0 -1 0 -2 2
0
Output:
[[-2, -1, 1, 2], [-2, 0, 0, 2], [-1, 0, 0, 1]]

</p>

Example 2:

Input:
5
2 2 2 2 2
8
Output:
[[2, 2, 2, 2]]

</p>

inputFormat

The input is given from \(stdin\) in the following format:

n
arr[0] arr[1] ... arr[n-1]
X

Where \(n\) is the number of elements, followed by \(n\) space-separated integers representing the array and an integer \(X\) representing the target sum.

outputFormat

Print to \(stdout\) the list of unique quadruplets (each quadruplet is a list of 4 integers) that sum up to \(X\). The output should exactly match the Python list representation.

## sample

6
1 0 -1 0 -2 2
0

[[-2, -1, 1, 2], [-2, 0, 0, 2], [-1, 0, 0, 1]]