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 N ('z'-'a')
using namespace std;
int n,ans,mp[N+1];
string str[501];

void mk_mp(int pos,int i,int j){
  while(i<=j&&!str[i][pos])i++;
  if(i>=j)return;
  int ni=i,ch=str[i][pos]-'a';

  while(i<j&&ch==str[++i][pos]-'a')if(str[i-1][pos+1]&&!str[i][pos+1])ans=0;
  mk_mp(pos+1,ni,i-1);

  int a=str[i][pos]-'a';
  if(ch!=a){
    mk_mp(pos,i,j);
    mp[ch]|=(1<<a|mp[a]);
    ans*=!(mp[ch]&1<<ch);
  }

}

int main(){
  while(cin>>n,n){
    memset(mp,0,sizeof(mp));
    for(int i=0;i<n;i++)cin>>str[i];
    ans=1;
    mk_mp(0,0,n-1);
    cout <<(ans? "yes":"no")<<endl;
  }
  return 0;
}