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 <vector>
#include <string>
#include <map>
#include <algorithm>

using namespace std;

bool dfs(int pos, int start, const vector<vector<int>> &graph, vector<bool> &visited) {
    if(visited[pos]) return false;

    visited[pos] = true;
    for(int v : graph[pos]) {
        if(v == start) return true;
        if(dfs(v, start, graph, visited)) return true;
    }
    return false;
}

bool solve() {
    int N;
    if(!(cin >> N)) return false;
    if(!N) return false;

    vector<string> v(N);
    for(int i = 0; i < N; ++i) {
        cin >> v[i];
    }
    vector<vector<int>> graph(26);
    for(int i = 0; i < N-1; ++i) {
        const string &s1 = v[i];
        const string &s2 = v[i+1];
        if(s1.size() > s2.size() && s1.substr(0, s2.size()) == s2) {
            cout << "no" << endl;
            return true;
        }
        for(int j = 0; j < s1.size() && j < s2.size(); ++j) {
            if(s1[j] != s2[j]) {
                graph[s1[j]-'a'].push_back(s2[j]-'a');
                break;
            }
        }
    }
    for(int i = 0; i < 26; ++i) {
        vector<bool> visited(26, false);
        if(dfs(i, i, graph, visited)) {
            cout << "no" << endl;
            return true;
        }
    }
    cout << "yes" << endl;
    return true;
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(0);

    while(solve()) ;
    return 0;
}