Codeforces 889B (Codeforces Round #445 Div. 1) Restoration of string 图论

B. Restoration of string

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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.

给出很多字符串，要求构造一个字符串，使得所有给出的字符串在这个串当中都是出现次数最多子串。输出长度最短的答案。如果有多个答案，输出字典序最小的。

首先，答案中每个字母最多出现一次。因为如果一个字母出现多次，那么这单个的字母就是出现次数最多的子串了。

接着，我们发现答案中的字母有一定的顺序，顺序必须和所给的若干个单词中的顺序一致。要求有序，我们想到了构造有向图进行拓扑排序，把每个字母当做不同的点，最多26个点，把每个单词当中的前一个字母c1向后一个字母c2连边，表示答案当中c1必须在c2前面。

实际上，因为顺序不能矛盾，所以构造的图去掉重边之后，只能是很多条链组成的森林，不能有环和自环，否则答案就是NO。

接着就遍历所有链，把这些链构成的若干个词连起来就是答案。

需要注意的是一个串长度为1的情况，这时若这单个的字母没有连边，可能会被答案忽略。特判把它加上就好了。

#include 
#include 
#include 
#include  
#include