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 <stdio.h>
#include <queue>
#include <iostream>
#include <stdlib.h>
#include <string>
#include <string.h>
#include <algorithm>
#include <cmath>
using namespace std;
char s[505][15];
struct edge{
    int v,next;
}e[10000];
int head[30];
int en;
void add(int u,int v)
{
    e[en].v=v;
    e[en].next=head[u];
    head[u]=en++;
}
bool vis[30];
bool dfs(int u)
{
    vis[u]=true;
    for(int i=head[u];i!=-1;i=e[i].next)
    {
        int v = e[i].v;
        if(vis[v])return true;
        if(dfs(v))return true;
    }
    vis[u]=false;
    return false;
}
bool has[30][30];
int main()
{
    //freopen("a.txt","r",stdin);
    int n;
    while(~scanf("%d",&n)&&n)
    {
        if(n==1)
        {
            char ss[15];
            scanf("%s",ss);
            printf("yes\n");
            continue;
        }
        int len=0;
        memset(s,0,sizeof(s));
        memset(head,-1,sizeof(head));
        en=0;
        for(int i=0;i<n;++i){
            scanf("%s",s[i]);
            len=max(len,(int)strlen(s[i]));
        }
        int same[2][505];
        bool flag = true;
        memset(has,false,sizeof(has));
        memset(same,0,sizeof(same));
        for(int i=0;i<len;++i)
        {
            int q=i&1;
            int now = 0;
            for(int j=1;j<n;++j)
            {
                if(same[q^1][j-1]==same[q^1][j])
                {
                    int a = s[j-1][i] - 'a';
                    int b = s[j][i] - 'a';

                    if(b<0&&a>=0){
                        flag=false;
                        same[q][j]=++now;
                    }
                    else if(a<0&&b<0){
                        same[q][j]=same[q][j-1];
                    }
                    else if(a<0&&b>=0)
                    {
                        same[q][j]=++now;
                    }
                    else if(a==b){
                        same[q][j]=same[q][j-1];
                    }
                    else{
                        if(!has[a][b])
                        {
                            has[a][b]=true;
                            add(a,b);
                        }
                        same[q][j]=++now;
                    }
                }
                else same[q][j]=++now;
            }
        }
        for(int i=0;i<26;++i){
            memset(vis,false,sizeof(vis));
            if(dfs(i))
            {
                flag=false;
                break;
            }
        }
        if(!flag)printf("no\n");
        else printf("yes\n");
    }
    return 0;
}