A substring of some string is called the most frequent, if the number of its occurrences is not less than number of occurrences of any other substring.

You are given a set of strings. A string (not necessarily from this set) is called good if all elements of the set are the most frequent substrings of this string. Restore the non-empty good string with minimum length. If several such strings exist, restore lexicographically minimum string. If there are no good strings, print "NO" (without quotes).

A substring of a string is a contiguous subsequence of letters in the string. For example, "ab", "c", "abc" are substrings of string "abc", while "ac" is not a substring of that string.

The number of occurrences of a substring in a string is the number of starting positions in the string where the substring occurs. These occurrences could overlap.

String a is lexicographically smaller than string b, if a is a prefix of b, or a has a smaller letter at the first position where a and b differ.

Input

The first line contains integer n (1 ≤ n ≤ 105) — the number of strings in the set.

Each of the next n lines contains a non-empty string consisting of lowercase English letters. It is guaranteed that the strings are distinct.

The total length of the strings doesn't exceed 105.

Output

Print the non-empty good string with minimum length. If several good strings exist, print lexicographically minimum among them. Print "NO" (without quotes) if there are no good strings.

Examples

Input

4
mail
ai
lru
cf


Output

cfmailru


Input

3
kek
preceq
cheburek


Output

NO

Note

One can show that in the first sample only two good strings with minimum length exist: "cfmailru" and "mailrucf". The first string is lexicographically minimum.
def generate_good_string(subs : list):
    In, Out, S = {}, {}, set()
    for s in subs:
        if len(s) == 1:
            S.add(s) 
        for fr, to in zip(s, s[1:]):
            if fr != In.get(to, fr) or to != Out.get(fr, to):
                return(print('NO'))
            Out[fr], In[to] = to, fr
    Outset, Inset = set(Out), set(In)
    S -= (set.union(Outset, Inset))
    for s in Outset - Inset:
        while Out.get(s[-1]):
            s += Out.pop(s[-1])
        S.add(s)
    print('NO' if Out else ''.join(sorted(S)))
substrings = [input() for _ in range(int(input()))]
generate_good_string(substrings)