A string w of parentheses ( and ) and brackets [ and ] is balanced if it satisfies one of the following conditions:

w is the empty string.

w = ( x ) for some balanced string x

w = [ x ] for some balanced string x

w = x y for some balanced strings x and y

For example, the string w = ([()][]())[()()]() is balanced, because w = xy, where x = ([()][]()) and y = [()()]() . Describe and analyze a dynamic programming algorithm to compute the length of a longest balanced subsequence of a given string of parentheses and brackets. Your input is an array w[1... n], where w[i] {(,),[,]} for every index i.