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Sum of Scores of Built Strings

You are building a string s of length n one character at a time, prepending each new character to the front of the string.

You are building a string s of length n one character at a time, prepending each new character to the front of the string. The strings are labeled from 1 to n, where the string with length i is labeled si.

The score of si is the length of the longest common prefix between si and sn (Note that s == sn).

Given the final string s, return the sum of the score of every si.

Sum of Scores of Built Strings diagram

Example 1

Input: s = "babab"

Output: 9

Explanation: For s1 == "b", the longest common prefix is "b" which has a score of 1. For s2 == "ab", there is no common prefix so the score is 0. For s3 == "bab", the longest common prefix is "bab" which has a score of 3. For s4 == "abab", there is no common prefix so the score is 0. For s5 == "babab", the longest common prefix is "babab" which has a score of 5. The sum of the scores is 1 + 0 + 3 + 0 + 5 = 9, so we return 9.

Example 2

Input: s = "azbazbzaz"

Output: 14

Explanation: For s2 == "az", the longest common prefix is "az" which has a score of 2. For s6 == "azbzaz", the longest common prefix is "azb" which has a score of 3. For s9 == "azbazbzaz", the longest common prefix is "azbazbzaz" which has a score of 9. For all other si, the score is 0. The sum of the scores is 2 + 3 + 9 = 14, so we return 14.

Constraints

  • 1 <= s.length <= 10^5
  • s consists of lowercase English letters.

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