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 main(){
  while (1){
    int n;
    cin >> n;
    if (n == 0){
      break;
    }
    vector<string> s(n);
    for (int i = 0; i < n; i++){
      cin >> s[i];
      s[i] += '{';
    }
    vector<set<int>> E(26);
    bool ok = true;
    for (int i = 0; i < n - 1; i++){
      if (s[i] != s[i + 1]){
        int c = 0;
        while (s[i][c] == s[i + 1][c]){
          c++;
        }
        if (s[i + 1][c] == '{'){
          ok = false;
        } else if (s[i][c] != '{'){
          E[s[i][c] - 'a'].insert(s[i + 1][c] - 'a');
        }
      }
    }
    if (!ok){
      cout << "no" << endl;
    } else {
      vector<int> deg(26, 0);
      for (int i = 0; i < 26; i++){
        for (int j : E[i]){
          deg[j]++;
        }
      }
      queue<int> Q;
      for (int i = 0; i < 26; i++){
        if (deg[i] == 0){
          Q.push(i);
        }
      }
      while (!Q.empty()){
        int v = Q.front();
        Q.pop();
        for (int w : E[v]){
          deg[w]--;
          if (deg[w] == 0){
            Q.push(w);
          }
        }
      }
      for (int i = 0; i < 26; i++){
        if (deg[i] != 0){
          ok = false;
        }
      }
      if (!ok){
        cout << "no" << endl;
      } else {
        cout << "yes" << endl;
      }
    }
  }
}
