Dictionary

Problem Statement

We found a dictionary of the Ancient Civilization Mayo (ACM) during excavation of the ruins. After analysis of the dictionary, we revealed they used a language that had not more than 26 letters. So one of us mapped each letter to a different English alphabet and typed all the words in the dictionary into a computer.

How the words are ordered in the dictionary, especially whether they are ordered lexicographically, is an interesting topic to many people. As a good programmer, you are requested to write a program to judge whether we can consider the words to be sorted in a lexicographical order.

Note: In a lexicographical order, a word always precedes other words it is a prefix of. For example, ab precedes abc, abde, and so on.

Input

The input consists of multiple datasets. Each dataset is formatted as follows:

n string_1 ... string_n

Each dataset consists of n+1 lines. The first line of each dataset contains an integer that indicates n (1 \leq n \leq 500). The i-th line of the following n lines contains string_i, which consists of up to 10 English lowercase letters.

The end of the input is 0, and this should not be processed.

Output

Print either yes or no in a line for each dataset, in the order of the input. If all words in the dataset can be considered to be ordered lexicographically, print yes. Otherwise, print no.

Example

Input

4 cba cab b a 3 bca ab a 5 abc acb b c c 5 abc acb c b b 0

Output

yes no yes no

inputFormat

Input

The input consists of multiple datasets. Each dataset is formatted as follows:

n string_1 ... string_n

Each dataset consists of n+1 lines. The first line of each dataset contains an integer that indicates n (1 \leq n \leq 500). The i-th line of the following n lines contains string_i, which consists of up to 10 English lowercase letters.

The end of the input is 0, and this should not be processed.

outputFormat

Output

Print either yes or no in a line for each dataset, in the order of the input. If all words in the dataset can be considered to be ordered lexicographically, print yes. Otherwise, print no.

Example

Input

4 cba cab b a 3 bca ab a 5 abc acb b c c 5 abc acb c b b 0

Output

yes no yes no

样例

4
cba
cab
b
a
3
bca
ab
a
5
abc
acb
b
c
c
5
abc
acb
c
b
b
0

yes
no
yes
no

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