Restoration of string

题意翻译

如果一个字符串的子串出现的次数大于任何子串出现的次数，那么这个子串就是 $\text{most frequent}$。 给 $n$ 个 $\text{most frequent}$ 子串，问最短的原串。 如果有多个最短原串，取字典序最小的那个。没有就输出 `NO`。

题目描述

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.

输入输出格式

输入格式

The first line contains integer $ n $ ( $ 1<=n<=10^{5} $ ) — 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 $ 10^{5} $ .

输出格式

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.

输入输出样例

输入样例 #1

4
mail
ai
lru
cf

输出样例 #1

cfmailru

输入样例 #2

3
kek
preceq
cheburek

输出样例 #2

NO

说明

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.