p01646 Dictionary
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
```python
def add_edge(node, adj_lst, s1, s2):
  ind = 0
  max_len = min(len(s1), len(s2))
  while ind < max_len and s1[ind] == s2[ind]:
    ind += 1
  if ind == max_len:
    return max_len < len(s1)

  c1 = ord(s1[ind]) - ord("a")
  c2 = ord(s2[ind]) - ord("a")
  adj_lst[c1].add(c2)
  node.add(c1)
  node.add(c2)
  return False

def visit(n, visited, adj_lst):
  ret = False
  if visited[n] == 2:
    return True
  elif visited[n] == 0:
    visited[n] = 2
    for to in adj_lst[n]:
      ret = ret or visit(to, visited, adj_lst)
    visited[n] = 1
  return ret
 
def main():
  while True:
    n = int(input())
    if n == 0:
      break
    
    lst = [input() for _ in range(n)]
    node = set()
    adj_lst = [set() for _ in range(26)]
    blank_flag = False
    for i in range(n):
      for j in range(i + 1, n):
        blank_flag = blank_flag or add_edge(node, adj_lst, lst[i], lst[j])
    if blank_flag:
      print("no")
      continue
    
    visited = [0] * 26
    cycle_flag = False
  
    for n in node:
      cycle_flag = cycle_flag or visit(n, visited, adj_lst)
    if cycle_flag:
      print("no")
    else:
      print("yes")

main()

```