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;

const int MAXN=555;
int n;
char str[MAXN][22];
int vis[255][255];
int in[255];
queue<int> q;

bool topsort()
{
    while(!q.empty())   q.pop();
    for(int i=0;i<255;i++)  if(in[i]==0)   q.push(i);
    int num=0;
    while(!q.empty())
    {
        int u=q.front();q.pop();num++;
        for(int i=0;i<255;i++)
            if(vis[u][i]==1)
            {
                in[i]--;
                if(in[i]==0)   q.push(i);
            }
    }
    return num==255;
}

bool check()
{
    memset(vis,0,sizeof vis);memset(in,0,sizeof in);
    for(int i=2;i<=n;i++)
    {
        for(int j=0;str[i][j] || str[i-1][j];j++)
        {
            if(str[i][j]==str[i-1][j])  continue;
            if(!str[i][j])    return false;
            int x=(int)(str[i-1][j]);
            int y=(int)(str[i][j]);
            if(vis[y][x])   return false;
            if(!vis[x][y])
            {
                vis[x][y]=1;
                in[y]++;
            }
            break;
        }
    }
    return topsort();
}


int main()
{
    //freopen("data.txt","r",stdin);
    while(cin>>n && n)
    {
        memset(str,0,sizeof str);
        for(int i=1;i<=n;i++)
            scanf("%s",str[i]);
//        for(int i=1;i<=n;i++)
//        {
//            int len=strlen(str[i]);
//            for(int j=0;j<len;j++)
//                if(str[i][j]>= 'a' && str[i][j]<='z')
//                    continue;
//                else
//                    while(1){}
//        }
        if(check())
            puts("yes");
        else
            puts("no");
    }
    return 0;
}