D. Restoration of string

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. [samples] ## 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.