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.
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  int s = 0;
  bool otv = true;
  string rez;
  map<char, pair<char, char> > graf;
  cin >> n;
  for (int i = 0; i < n; i++) {
    string st;
    cin >> st;
    for (int j = 0; j < st.length(); j++) {
      if (graf.count(st[j]) == 0) {
        s++;
        if ((j > 0) && (j < st.length() - 1)) {
          graf.insert(pair<char, pair<char, char> >(
              st[j], pair<char, char>(st[j - 1], st[j + 1])));
        } else if (j > 0) {
          graf.insert(pair<char, pair<char, char> >(
              st[j], pair<char, char>(st[j - 1], ' ')));
        } else if (j < st.length() - 1) {
          graf.insert(pair<char, pair<char, char> >(
              st[j], pair<char, char>(' ', st[j + 1])));
        } else
          graf.insert(
              pair<char, pair<char, char> >(st[j], pair<char, char>(' ', ' ')));
      } else {
        if ((((graf.find(st[j])->second.second != ' ') &&
              (j != st.length() - 1)) &&
             (graf.find(st[j])->second.second != st[j + 1])) ||
            (((graf.find(st[j])->second.first != ' ') && (j != 0)) &&
             (graf.find(st[j])->second.first != st[j - 1])))
          otv = false;
        if ((j > 0) && (j < st.length() - 1)) {
          graf.at(st[j]) = pair<char, char>(st[j - 1], st[j + 1]);
        } else if (j > 0) {
          graf.at(st[j]) =
              pair<char, char>(st[j - 1], graf.find(st[j])->second.second);
        } else if (j < st.length() - 1) {
          graf.at(st[j]) =
              pair<char, char>(graf.find(st[j])->second.first, st[j + 1]);
        } else
          graf.at(st[j]) = pair<char, char>(graf.find(st[j])->second.first,
                                            graf.find(st[j])->second.second);
      }
    }
  }
  if (otv) {
    map<char, pair<char, char> >::iterator j;
    j = graf.begin();
    for (int i = 0; i < 27, j != graf.end(); j++) {
      if (j->second.first == ' ') {
        char q = j->first;
        while (q != ' ') {
          i++;
          rez += q;
          q = graf.find(q)->second.second;
          if (i >= 28) {
            i = 28;
            break;
          };
        }
      }
      if (i == 28) {
        otv = false;
        break;
      };
      i = 0;
    }
  }
  if (rez.length() != s) otv = false;
  if (otv) {
    cout << rez;
  } else
    cout << "NO";
  return 0;
}
