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
#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
using namespace std;

int main(){
    int N;
    while(cin>>N,N){
        vector<string> S(N);
        for(auto &s:S) cin>>s;
        int G[26][26];
        fill(G[0],G[26],0);
        bool flag=true;
        for(int i=0;i<N;i++){
            for(int j=i+1;j<N;j++){
                string s1=S[i], s2=S[j];
                if(s1==s2) continue;
                int ite=0;
                while(ite<min(s1.size(),s2.size())&&s1[ite]==s2[ite]) ite++;
                if(ite==s1.size()) continue;
                if(ite==s2.size()){
                    flag=false;
                    continue;
                }
                G[s1[ite]-'a'][s2[ite]-'a']=1;
            }
        }
        for(int k=0;k<26;k++){
            for(int i=0;i<26;i++){
                for(int j=0;j<26;j++){
                    G[i][j]|=G[i][k]&G[k][j];
                }
            }
        }
        for(int i=0;i<26;i++){
            if(G[i][i]) flag=false;
        }
        cout<<(flag?"yes":"no")<<endl;
    }

    return 0;
}
