The operating system of your computer indexes the files on your hard disk based on their contents, and provides textual search over them. The content of each file is a non-empty string of lowercase letters. To do a search, you specify a key, which is also a non-empty string of lowercase letters. The result is a list of all the files that contain the key as a substring. A string \textbf{s} is a substring of a string \textbf{t} if \textbf{t} contains all characters of \textbf{s} as a contiguous sequence. For instance, "\textbf{foofoo}", "\textbf{cafoo}", "\textbf{foota}" and "\textbf{foo}" all contain "\textbf{foo}" as a substring, while "\textbf{foa}", "\textbf{fofo}", "\textbf{ oo}" and "\textbf{oofo}" do not. You know the content of each file on your hard disk, and wonder whether each subset of the les is searchable. A subset of the files is searchable if there exists at least one key that produces exactly the list of those files as a result. Given the contents of the files on your hard disk, you are asked to compute the number of non-empty searchable subsets. \InputFile Each test case is described using several lines. The first line contains an integer \textbf{F} representing the number of files on your hard disk (\textbf{1} ≤ \textbf{F} ≤ \textbf{60}). Each of the next \textbf{F} lines indicates the content of one of the files. The content of a file is a non-empty string of at most \textbf{10^4} characters; each character is one of the \textbf{26} standard lowercase letters (from '\textbf{a}' to '\textbf{z}'). The last test case is followed by a line containing one zero. \OutputFile For each test case output a line with an integer representing the number of non-empty searchable subsets.