Strings are basically "words in computers". As an ordered set of characters, these are the building blocks that allow us to do things from searching filesystems to decrypting ciphers.

Substitution: Replacing a single character from \(a\) so that it matches \(b\) costs \(1\). If \(a=\text{rot}\) and \(b=\text{dot}\). Then \(f(a,b)=1\).

Insertion: Inserting a single character also costs \(1\). Ie, If \(a = \text{girl}\) and \(b=\text{girls}\), then \(f(a,b)=1\).

Deletion: Deleting a single character also costs \(1\). Ie. If \(a=\text{hour}\) and \(b=\text{our}\) then \(f(a,b)=1\).

Given \(a\) and \(b\), compute \(f(a,b)\).

Let the **reverse** of a positive integer \(n\), denoted \(R(n),\) be the result when the digits of the number are written backwards; for example, \(R(190) = 091,\) or just \(91.\)

Call a positive integer \(n\) **brilliant** if \[n + R(n)\]

is a multiple of 13. Let \(B\) be the \(10000\)th brilliant number. Compute the last three digits of \(B.\)

**PalPrime** is a prime number that is also a palindrome.The first few PalPrimes are \(2, 3, 5, 7, 11, 101, 131, 151, 181, 191...\). Let \(S\) be the sum of the digits of the largest PalPrime \(N\) such that \(N<10^9\).What is the value of \(S\)?

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