Find the next closest largest palindrome of a given number

Work with digit characters because the input may exceed native integer range. Mirror the left half onto the right first; this gives the closest palindrome sharing the left prefix. If it is already on the needed side of the original number, it is a candidate. Otherwise adjust the middle digit or left-middle prefix by one, propagate carry or borrow leftward, and mirror again. For a nearest different palindrome, generate both lower and higher candidates and compare numeric distance, with a stated tie rule. Boundary cases are where most bugs live: 9 maps around to 8 and 11, 10 to 9 and 11, 99 to 101, and 1000 to 999 and 1001. Clarify whether the question asks next larger, next smaller, or nearest. Comparing equal-length strings is lexicographic; use string subtraction or careful digit comparison for distances. Each candidate is built in O(n) time and O(n) space.