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 <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
using namespace std;

vector<int> cc[30];
char a[510][32];
int n;
bool vis[26], can[26];

bool init()
{
    memset(vis, 0, sizeof(vis));
    memset(can, 0, sizeof(can));
    for(int i = 0; i < 26; ++ i) cc[i].clear();
    for(int i = 1; i < n; ++ i)
    {
        int j, len = min(strlen(a[i]), strlen(a[i-1]));
        for(j = 0; j < len; ++ j)
            if(a[i][j] != a[i-1][j]) break;
        if(strlen(a[i-1]) > strlen(a[i])  && j >= len) return false;
        if(j < len) cc[a[i][j] - 'a'].push_back(a[i-1][j] - 'a');
    }
    for(int i = 0; i < 26; ++ i)
    {
        sort(cc[i].begin(), cc[i].end());
        cc[i].erase(unique(cc[i].begin(), cc[i].end() ), cc[i].end());
    }
    return true;
}

bool dfs(int cur)
{
    vis[cur] = true;
    if(can[cur]) return false;
    can[cur] = true;
    for(int i = 0; i < (int)cc[cur].size(); ++ i)
        if(!dfs(cc[cur][i])) return false;
    can[cur] = false;
    return true;
}

int main()
{
    while(scanf("%d", &n) == 1 && n)
    {
        for(int i = 0; i < n; ++ i)
            scanf("%s", a[i]);
        if(!init())
        {
            puts("no");
            continue;
        }
        bool flag = 1;
        for(int i = 0; i < 26; i++)
        {
            if(!vis[i] && !dfs(i))
            {
                flag = 0;
                break;
            }
        }
        if(flag) puts("yes");
        else puts("no");
    }
    return 0;
}