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>
using namespace std;

int g[30][30];

int main(){
  int n;
  while(cin >> n, n){
    vector<string> s(n);
    for(int i=0;i<n;i++)cin >> s[i];

    for(int i=0;i<26;i++){
      for(int j=0;j<26;j++){
	  g[i][j] = 1e9;
      }
      g[i][i] = 0;
    }

    bool f = true;
    for(int i=1;i<n;i++){
      int len = min(s[i-1].size(), s[i].size()), j;
      for(j=0;j<len;j++){
	if(s[i-1][j]!=s[i][j])break;
      }

      if(j==len){
	if(s[i-1].size() > s[i].size()){
	  f = false;
	}
      }else{
	g[s[i-1][j]-'a'][s[i][j]-'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] = min(g[i][j], g[i][k] + g[k][j]);
	}
      }
    }

    for(int i=0;i<26;i++){
      if(g[i][i] < 0) f = false;
    }

    cout << (f?"yes":"no") << endl;
  }   
}