You are given two strings s and target, both having length n, consisting of lowercase English letters.

Return the lexicographically smallest permutation of s that is strictly greater than target. If no permutation of s is lexicographically strictly greater than target, return an empty string.

A string a is lexicographically strictly greater than a string b (of the same length) if in the first position where a and b differ, string a has a letter that appears later in the alphabet than the corresponding letter in b.

Example 1:

Input: s = "abc", target = "bba"

Output: "bca"

Explanation:

The permutations of s (in lexicographical order) are "abc", "acb", "bac", "bca", "cab", and "cba".
The lexicographically smallest permutation that is strictly greater than target is "bca".

Example 2:

Input: s = "leet", target = "code"

Output: "eelt"

Explanation:

The permutations of s (in lexicographical order) are "eelt", "eetl", "elet", "elte", "etel", "etle", "leet", "lete", "ltee", "teel", "tele", and "tlee".
The lexicographically smallest permutation that is strictly greater than target is "eelt".

Example 3:

Input: s = "baba", target = "bbaa"

Output: ""

Explanation:

The permutations of s (in lexicographical order) are "aabb", "abab", "abba", "baab", "baba", and "bbaa".
None of them is lexicographically strictly greater than target. Therefore, the answer is "".

Constraints:

1 <= s.length == target.length <= 300
s and target consist of only lowercase English letters.