Given a string of characters, find the length of the longest proper prefix which is also a proper suffix.

NOTE: Prefix and suffix can be overlapping but they should not be equal to the entire string.

Example 1:

Input: s = "abab"
Output: 2
Explanation: "ab" is the longest proper 
prefix and suffix. 

Example 2:

Input: s = "aaaa"
Output: 3
Explanation: "aaa" is the longest proper 
prefix and suffix. 

Your task:
You do not need to read any input or print anything. The task is to complete the function lps(), which takes a string as input and returns an integer.

Expected Time Complexity: O(|s|)
Expected Auxiliary Space: O(|s|)

Constraints:
1 ≤ |s| ≤ 10⁵
s contains lower case English alphabets