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<bits/stdc++.h>
#define r(i,n) for(int i=0;i<n;i++)
using namespace std;
string s[501];
int d[26][26],n;
int main(){
  while(cin>>n,n){
    int ans=0,f=0;
    r(i,26)r(j,26)d[i][j]=1e8;
    r(i,n)cin>>s[i];
    r(i,n-1){
      r(j,s[i].size()){
        if(j>=s[i+1].size()){f++;break;}
        if(s[i][j]!=s[i+1][j]){
            d[s[i][j]-'a'][s[i+1][j]-'a']=-1;
            break;
        }
      }
    }
    r(k,26)r(i,26)r(j,26)d[i][j]=min(d[i][j],d[i][k]+d[k][j]);
    r(i,26)if(d[i][i]<0)ans++;
    cout<<(ans||f?"no":"yes")<<endl;
  }
}