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>
using namespace std;
int INF = 1e9;

bool has_loop(vector< vector<int> > G){
  int n = G.size();
  for(int k = 0; k < n; ++k){
    for(int i = 0; i < n; ++i){
      for(int j = 0; j < n; ++j){
        G[i][j] = min(G[i][j],G[i][k] + G[k][j]);
      }
    }
  }
  for(int i = 0; i < n; ++i){
    if(G[i][i] < INF) return true;
  }
  return false;
}

int main(){
  int n;
  while(cin >> n, n){
    vector<string> S(n);
    for(int i = 0; i < n; ++i){
      cin >> S[i];
    }
    if(n == 1){
      cout << "yes" << endl;
      continue;
    }
    vector< vector<int> > G(26, vector<int>(26,INF));
    bool f = true, g = false;
    for(int i = 1; i < n; ++i){
      if(S[i-1] == S[i]) continue;
      for(int j = 0; j < min(S[i].length(),S[i-1].length()); ++j){
        f = true;
        if(S[i][j] != S[i-1][j]){
          //G[S[i-1][j] - 'a'].push_back(S[i][j] - 'a');
          G[S[i-1][j] - 'a'][S[i][j] - 'a'] = 1;
          f = false;
          break;
        }
      }
      if(f && S[i-1].size() > S[i].size()){
        cout << "no" << endl;
        g = true;
        break;
      }else{
        f = false;
      }
    }
    if(g) continue;

    if(has_loop(G)) cout << "no" << endl;
    else cout << "yes" << endl;
  }
  return 0;
}

