Determine validity after digit-constrained deletions

You're given a string S of length n consisting only of '(' , ')' , and digits '0'–'9'. For every digit at index i with numeric value v: ( 1) you must delete exactly v parentheses that occur at indices strictly less than i; ( 2) a given parenthesis can be deleted at most once across all digits; ( 3) digits themselves are not deleted and should be ignored when checking validity. After choosing deletions for all digits, consider the sequence of remaining parentheses (ignoring digits). Return true if there exists at least one choice of deletions such that the remaining parentheses form a valid parentheses string, otherwise return false. Also describe an efficient algorithm, its time and space complexity, and optionally output one valid witness set of deletions if it exists.