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 <cstdio>
#include <iostream>
#include <vector>
#include <string>
#include <stack>
#define rep(i,a,n) for(int i=a; i<n; i++)
using namespace std;

// 移動元と行先と辺のコストを記録する構造体
template <typename T>
struct Edge {
    int from, to;
    T cost;
    Edge(int s, T d) : to(s), cost(d) {}
    Edge(int f, int s, T d) : from(f), to(s), cost(d) {}

    bool operator<(const Edge &e) const {
        return cost < e.cost;
    }
    bool operator>(const Edge &e) const {
        return cost > e.cost;
    }
};

template <typename T>
using Graph = vector< vector< Edge<T> > >;

template <typename T>
vector<int> tpsort_Kahn(const vector< vector< Edge<T> > > &g) {
    const int V = g.size();
    vector<int> indeg(V, 0);
    stack<int> S;

    rep(i,0,V) rep(j,0,g[i].size())
        indeg[ g[i][j].to ]++;
    rep(i,0,V) if(indeg[i] == 0) S.push(i);

    vector<int> ans;
    while(S.size() > 0) {
        int u = S.top(); S.pop();
        ans.push_back(u);
        rep(i,0,g[u].size()) {
            indeg[ g[u][i].to ]--;
            if(indeg[ g[u][i].to ] ==  0)
                S.push( g[u][i].to );
        }
    }
    return ans;
}


int main() {
    int N;
    while(cin >> N, N) {
        vector<string> vs(N);
        for(int i=0; i<N; i++) {
            cin >> vs[i];
        }

        bool ok = true;
        Graph<int> G(26);
        for(int i=0; i<N; i++) {
            for(int j=i+1; j<N; j++) {
                int S = min(vs[i].length(), vs[j].length());
                bool differ = false;
                for(int k=0; k<S; k++) {
                    if(vs[i][k] != vs[j][k]) {
                        differ = true;
                        int u = vs[i][k] - 'a', v = vs[j][k] - 'a';
                        G[u].push_back(Edge<int>(v, 1));
                        break;
                    }
                }
                if(!differ && vs[i].length() > vs[j].length()) ok = false;
            }
        }
        
        if(tpsort_Kahn(G).size() == 26 && ok) cout << "yes" << endl;
        else cout << "no" << endl;
    }
    return 0;
}
