Remove Boxes

Keep matching boxes available for a merge

Define dp(l, r, k) as the maximum score for boxes l..r when k boxes equal to boxes[l] are already attached on its left. First absorb equal boxes at l into k. Remove that enlarged run now for (k+1)^2, or for every later matching color m, remove the middle and solve it with the carried group merged at m. The carry state captures the future value lost by greedy deletion. Memoization bounds states to O(n³) with up to O(n) transitions, commonly O(n⁴) time and O(n³) space. Test one color, separated matching colors, a middle run worth removing, and score overflow. A plain two-index interval DP cannot represent the merge benefit.