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 <iostream>
#include <string>
#include <sstream>
#include <stack>
#include <algorithm>
#include <cmath>
#include <queue>
#include <map>
#include <set>
#include <cstdlib>
#include <bitset>
#include <tuple>
#include <assert.h>
#include <deque>
#include <bitset>
#include <iomanip>
#include <limits>
#include <chrono>
#include <random>
#include <array>
#include <unordered_map>
#include <functional>
#include <complex>
#include <numeric>
#include <cctype>


template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
//constexpr long long MAX = 5100000;
constexpr long long INF = 1LL << 60;
constexpr int inf = 1000000007;
constexpr long long mod = 1000000007LL;
//constexpr long long mod = 998244353LL;
const long double PI = acos((long double)(-1));

using namespace std;
typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;

vector<int> topological(vector<vector<int>>& g) {
	vector<int> topo;
	int n = g.size();
	vector<int> deg(n);
	for (int i = 0; i < n; i++) for (auto next : g[i]) deg[next]++;
	queue<int> q;
	for (int i = 0; i < n; i++) if (deg[i] == 0) q.push(i), topo.push_back(i);
	while (!q.empty()) {
		int cur = q.front();
		q.pop();
		for (auto next : g[cur]) {
			deg[next]--;
			if (deg[next] == 0) {
				q.emplace(next);
				topo.push_back(next);
			}
		}
	}
	return topo;
}

void solve() {
	int n; cin >> n; if (n == 0) exit(0);
	vector<string> vs(n);
	for (int i = 0; i < n; i++) cin >> vs[i];
	vector<vector<int>> g(26);
	for (int i = 0; i + 1 < n; i++) {
		string& s = vs[i];
		string& t = vs[i + 1];
		bool u = false;
		for (int j = 0; j < min(s.size(), t.size()); j++) {
			if (s[j] != t[j]) {
				g[s[j] - 'a'].emplace_back(t[j] - 'a');
				u = true;
				break;
			}
		}
		if (!u and s.size() > t.size()) {
			cout << "no" << "\n";
			return;
		}
	}

	auto t = topological(g);
	if (t.size() == 26) cout << "yes" << "\n";
	else cout << "no" << "\n";
}

int main()
{

	cin.tie(nullptr);
	ios::sync_with_stdio(false);

	int kkt = 89;
	while (kkt) {
		solve();
	}
}
