class Node:
    def __init__(self, name, value=None):
        self.name = name
        self.value = value
        self.children = []

    def add_child(self, child):
        self.children.append(child)

    def __repr__(self):
        return str(self)

    def __str__(self):
        res = self.name
        if self.value is not None:
            res += f'[{self.value}]'

        if len(self.children) > 0:
            res += '('
            sep = ''

            for child in self.children:
                res += sep + str(child)
                sep = ','
            res += ')'
        return res

    def copy(self):
        node = Node(self.name, self.value)
        for child in self.children:
            node.add_child(child.copy())
        return node

    def remove_quant(self, name):
        if self.name == name:
            itr = self
            while itr.name == name:
                itr = itr.children[1]
            return itr

        node = Node(self.name, self.value)
        for child in self.children:
            if child.name == name:
                node.add_child(child.children[1].remove_quant(name))
            else:
                node.add_child(child.remove_quant(name))
        return node

    def subst(self, values):
        node = Node(self.name, self.value)
        if self.name == 'VAR' and self.value in values.keys():
            node = values[self.value]
        else:
            for child in self.children:
                node.add_child(child.subst(values))

        return node

    def equals(self, rhs):
        if self.name != rhs.name or self.value != rhs.value:
            return False

        if len(self.children) != len(rhs.children):
            return False

        for i in range(len(self.children)):
            if not self.children[i].equals(rhs.children[i]):
                return False

        return True