A string s holds lowercase letters and the round brackets ( and ). Delete as few brackets as possible so that the brackets left are balanced: each ) closes an earlier (, and each ( is closed by a later ). In counting terms: reading left to right, the ) never outnumber the ( so far, and at the end the two counts are equal.

Keep every letter, keep the characters that remain in their original order, and return the resulting string. When several strings need the same smallest number of deletions, return any one of them. A string with no brackets, including the empty string, is already balanced.