Canadian Computing Competition: 2004 Stage 1, Senior #1

A collection of words is prefix-free if no word is a prefix of any other word. A collection of words is suffix-free if no word is a suffix of any other word. A collection of words is fix-free if it is both prefix-free and suffix-free.

For this problem, a word is a sequence of lower-case letters of length between \(1\) and \(25\) . A word \(X\) is a prefix of word \(Y\) if \(X\) consists of the first \(n\) characters of \(Y\) , in order, for some \(n\) . That is, the word cat has prefixes c , ca , and cat . Similarly, a word \(X\) is a suffix of \(Y\) if \(X\) consists of the last \(n\) characters of \(Y\) , in order, for some \(n\) .

Your input will be \(3N+1\) lines: the first line will be the number \(N\) , and the remaining \(3N\) lines will be the \(N\) collections of \(3\) words each. (That is, lines \(2\) , \(3\) , and \(4\) compose the first collection, lines \(5\) , \(6\) , and \(7\) compose the second collection, and so on). Your output will be \(N\) lines, each line containing either Yes (if that collection of words is fix-free) or No (if that collection is not fix-free).

Sample Input

2
abba
aab
bab
a
ab
aa

Sample Output

Yes
No