In this problem, you have to perform operations with sets according to the given expression. Consider an expression involving three sets \textbf{A}, \textbf{B} and \textbf{C} and three set operations: union, intersection and complement. For the purposes of this problem, sets can only consist of numbers \{\textbf{1}, \textbf{2}, ... , \textbf{n}\} for some fixed integer \textbf{n}. A union of sets \textbf{X} and \textbf{Y} is a set which contains all numbers present in at least one of the sets \textbf{X} and \textbf{Y}. An intersection of sets \textbf{X} and \textbf{Y} is a set which contains all numbers present in both of the sets \textbf{X} and \textbf{Y} . A complement of set \textbf{X} is a set which contains all numbers from the range \{\textbf{1}, \textbf{2}, ... , \textbf{n}\} which are not in \textbf{X}. For example, if \textbf{n} = \textbf{5}, \textbf{X} = \{\textbf{3}, \textbf{4}\} and \textbf{Y} = \{\textbf{1}, \textbf{3}\}, the union of \textbf{X} and \textbf{Y} is \{\textbf{1}, \textbf{3}, \textbf{4}\}, their intersection is \{\textbf{3}\}, and complement of \textbf{X} is \{\textbf{1}; \textbf{2}; \textbf{5}\}. An expression is recursively defined as follows: \begin{itemize} \item \textbf{A}, \textbf{B} and \textbf{C} are expressions denoting the three given sets \textbf{A}, \textbf{B} and \textbf{C} respectively. \item If \textbf{E} is an expression, ~\textbf{E} and (\textbf{E}) are also expressions. \item If \textbf{E} and \textbf{F} are expressions, \textbf{E }| \textbf{F} and \textbf{E} & \textbf{F} are also expressions. \end{itemize} Here, ~\textbf{X} is the complement of set \textbf{X}, \textbf{X} | \textbf{Y} is the union of sets \textbf{X} and \textbf{Y} , and \textbf{X} & \textbf{Y} is the intersection of sets \textbf{X} and \textbf{Y}. Complement is evaluated before intersection, which in turn is evaluated before union. Parentheses play the usual role of prioritizing operations. So, for example, an expression \textbf{A} | ~\textbf{B} & \textbf{C} is evaluated in the same way as \textbf{A} | ((~\textbf{B}) & \textbf{C}). You are given one expression and a number of triples of sets \textbf{A}, \textbf{B} and \textbf{C}. Find and output the value of the expression for each of the given triples. \InputFile The first line contains the expression. Its length is from \textbf{1} to \textbf{300 000} characters. It is guaranteed that the expression conforms with the recursive definition above. There are no spaces on the first line. The second line contains two integers \textbf{n} and \textbf{t} (\textbf{1} ≤ \textbf{n} ≤ \textbf{20}, \textbf{1} ≤ \textbf{t} ≤ \textbf{10 000}) separated by a space: the number of elements and the number of triples of sets. Each of the next \textbf{t} lines describes a triple of sets \textbf{A}, \textbf{B} and \textbf{C} in that order. A set is denoted by a list of integers contained in that set in strictly ascending order followed by a zero. Numbers are separated by one or more spaces. \OutputFile For each of the \textbf{t} given triples of sets, output a single line containing a single set: the result of evaluating the expression for the given \textbf{A}, \textbf{B} and \textbf{C}. A set must be written as a list of integers contained in that set in strictly ascending order followed by a zero. Separate numbers by one space.