Valid Strings-erase the smallest possible number of characters such that the remaining string after the erasures is valid

A string over the characters (, [, ] and ) is said to be valid if one can reduce the string to the null string by repeatedly erasing two consecutive characters of the form () or []. For example, the string [([])[]] is valid but neither ([)] nor ([ is valid.
Give a polynomial time algorithm to solve the following problem: Given a string, erase the smallest possible number of characters such that the remaining string after the erasures is valid. For example, given the string [(], we can erase ( to get [].