Define a Uniform tree as one in which all of the nodes at a given level (i.e. distance from the root) have the same degree (i.e. number of children). Since all of the nodes at a given level have the same number of children, a uniform tree can be represented as simply a list of integers, indicating the number of children at each level. For example, the list \textbf{\[2 3 5 0\]} represents a tree where the root has 2 children, each child of the root has \textbf{3} children, each grandchild has \textbf{5} children, and each great-grandchild has no children, and is therefore a leaf. For the purposes of this problem, redefine Subtree as a connected subgraph of a tree that includes the tree’s root. This is a bit different than the typical definition of Subtree. Given a description of a tree, find all of the unique Uniform Subtrees of that tree. For example, here is a tree and all of its unique uniform subtrees: \includegraphics{https://static.e-olymp.com/content/c8/c8ece22671814c11a2ad3edfe5926c05e3a9c8e5.jpg} \InputFile There will be several test cases in the input. Each test case will will consist of a single tree, represented as a single string on one line. The string will be a sequence of matched opening and closing parentheses. Each matched pair represents a node, and the string between represents its children. There will not be more than \textbf{4000} nodes in the tree. There will be no whitespace, or any other characters, in the string. The input will end with a line with a single \textbf{0}. \OutputFile For each test case, output every unique uniform subtree of the given tree as a list of integers, one subtree (and thus one list) per line. Print a single space between integers, and no spaces anywhere else. Do not print any blank lines between lists, or between test cases. Print the lists for a given test case sorted by the first element, then the second, then the third, and so on.