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Given a **non-empty** string, encode the string such that its encoded length is the shortest.

The encoding rule is: `k[encoded_string]`

, where the *encoded_string* inside the square brackets is being repeated exactly *k* times.

**Note:**

*k*will be a positive integer and encoded string will not be empty or have extra space.- You may assume that the input string contains only lowercase English letters. The string's length is at most 160.
- If an encoding process does not make the string shorter, then do not encode it. If there are several solutions, return any of them is fine.

**Example 1:**

Input: "aaa" Output: "aaa" Explanation: There is no way to encode it such that it is shorter than the input string, so we do not encode it.

**Example 2:**

Input: "aaaaa" Output: "5[a]" Explanation: "5[a]" is shorter than "aaaaa" by 1 character.

**Example 3:**

Input: "aaaaaaaaaa" Output: "10[a]" Explanation: "a9[a]" or "9[a]a" are also valid solutions, both of them have the same length = 5, which is the same as "10[a]".

**Example 4:**

Input: "aabcaabcd" Output: "2[aabc]d" Explanation: "aabc" occurs twice, so one answer can be "2[aabc]d".

**Example 5:**

Input: "abbbabbbcabbbabbbc" Output: "2[2[abbb]c]" Explanation: "abbbabbbc" occurs twice, but "abbbabbbc" can also be encoded to "2[abbb]c", so one answer can be "2[2[abbb]c]".

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