B'A bracket sequence is a string containing only characters "(" and ")". A regular bracket sequence (or, shortly, an RBS) is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters "1" and "+" between the original characters of the sequence. For example: Let 's denote the concatenation of two strings x and y as x+y . For example, "()()" + ")(" = "()())(". You are given n bracket sequences s_1, s_2, ... , s_n . You can rearrange them in any order (you can rearrange only the strings themselves, but not the characters in them). Your task is to rearrange the strings in such a way that the string s_1 + s_2 + ... + s_n has as many non-empty prefixes that are RBS as possible. The first line contains a single integer n ( 1 <= n <= 20 ). Then n lines follow, the i -th of them contains s_i -- a bracket sequence (a string consisting of characters "(" and/or ")". All sequences s_i are non-empty, their total length does not exceed 4 cdot 10^5 . Print one integer -- the maximum number of non-empty prefixes that are RBS for the string s_1 + s_2 + ... + s_n , if the strings s_1, s_2, ... , s_n can be rearranged arbitrarily. In the first example, you can concatenate the strings as follows: "(" + ")" = "()", the resulting string will have one prefix, that is an RBS: "()". In the second example, you can concatenate the strings as follows: "(" + ")" + "()()())" + "(" = "()()()())(", the resulting string will have four prefixes that are RBS: "()", "()()", "()()()", "()()()()". The third and the fourth examples contain only one string each, so the order is fixed. '...