Problem C

Filling the Gaps

At the largest conference on coding and cryptography the following theorem needed a proof or a counterexample: Suppose you are given a set of words of equal length; each word consisting of 0's, 1's and/or *'s. Furthermore suppose the pattern of *'s is different for all words in the set. By this we mean: if you replace all 0's and 1's by say $ you obtain different words.

The claim is: if you replace the *'s by 0's and 1's in all possible ways, then you obtain a set that is at least as big as the set you started with.

Example:

{ 10*, *0*, *00 } produces { 100, 101, 000, 001 }

{ 100, 101, 10* } produces { 100, 101 }

Notice that the set in the latter example does not satisfy the condidtion mentioned above, so it does not provide a counterexample.

You program has to check for a number of cases:

Whether the pattern of *'s is different for all words in the set and:
Compute the number of words obtained by replacing the *'s by 0's and 1's.

The words will not be longer than 15 symbols.

Input

The input is a text-file that presents a sequence of sets. Each set is described as follows. The first line gives two integers: the length of the words and the number of the words. Then follow the words, each on a separate line. The end of the sequence of sets is indicated by a set with wordlength 0 and number of words equal to 0.

Output

The output is a textfile that contains one line for each set. if the pattern of *'s is different for all the words in this set this line should contain YES (in uppercase), followed by a space and the number of obtained words, otherwise it should contain NO (uppercase) only.

Sample Input

Sample Output

YES 4
NO
YES 0