Given an array `S`

of `n`

integers, are there elements `a, b, c, and d`

in `S`

such that `a + b + c + d = target`

? Find all unique quadruplets in the array which gives the sum of target.

Note:

- Elements in a quadruplet (a,b,c,d) must be in non-descending order. (ie, a ≤ b ≤ c ≤ d)
- The solution set must not contain duplicate quadruplets.

**Example :**

Given array `S = {1 0 -1 0 -2 2}`

, and `target = 0`

A solution set is:

```
(-2, -1, 1, 2)
(-2, 0, 0, 2)
(-1, 0, 0, 1)
```

Also make sure that the solution set is lexicographically sorted.

`Solution[i] < Solution[j] iff Solution[i][0] < Solution[j][0] OR (Solution[i][0] == Solution[j][0] AND ... Solution[i][k] < Solution[j][k])`

NOTE:You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.

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