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John and Brus are studying string theory at the university. Brus likes palindromes very much. A palindrome is a word that reads the same forward and backward. John would like to surprise Brus by taking a String s, and appending 0 or more characters to the end of s to obtain a palindrome. He wants that palindrome to be as short as possible. Return the shortest possible length of a palindrome that..

The digits 3 and 9 share an interesting property. If you take any multiple of 3and sum its digits, you get another multiple of 3. For example 3 * 118 = 354 and 3 + 5 + 4 = 12, which is a multiple of 3. Similarly, if you take any multiple of 9 and sum its digits, you get another multiple of 9. A digit that is interesting in one base(진법) is not necessarily interesting in another base. For example,..