You're given a string of characters and a limit on how many times each character can repeat consecutively. Build the lexicographically largest string possible while respecting this repeat limit.

Find the number of ways to color an N by 3 grid using three different colors. No two adjacent cells, sharing a side, can have the same color.

Determine if a string is a palindrome after removing at most one character. Consider both left and right removals when checking for palindrome validity.