Given a list of phone numbers, determine if it is consistent in the sense that no number is the pre?x of another. Lets say the phone catalogue listed these numbers:

? Emergency 911

? Alice 97 625 999

? Bob 91 12 54 26

In this case, its not possible to call Bob, because the central would direct your call to the emergency line as soon as you had dialled the ?rst three digits of Bobs phone number. So this list would not be consistent.

Input

The ?rst line of input gives a single integer, 1 ? t ? 40, the number of test cases. Each test case starts with n, the number of phone numbers, on a separate line, 1 ? n ? 10000. Then follows n lines with one unique phone number on each line. A phone number is a sequence of at most ten digits.

Output

For each test case, output YES if the list is consistent, orNO otherwise.

Examples

Input

2

3

911

97625999

91125426

5

113

12340

123440

12345

98346

Output

NO

YES