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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])`

- Hint 1
- Hint 2
- Solution Approach
- Complete Solution

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