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 DFS(int);
vector<unordered_set<int> > a;
int n, u['z' + 1];
string s;
unordered_set<char> st;
unordered_set<char> sym;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cin >> n;
  a.resize('z' + 1);
  for (int i = 0; i < n; i++) {
    string t;
    cin >> t;
    st.insert(t[0]);
    sym.insert(t[0]);
    for (int j = 0; j < t.size() - 1; j++) {
      a[t[j]].insert(t[j + 1]);
      if (a[t[j]].size() > 1) {
        cout << "NO";
        return 0;
      }
      sym.insert(t[j + 1]);
    }
  }
  for (int i = 'a'; i < 'z' + 1; i++)
    for (auto j = st.begin(); j != st.end(); j++)
      if (a[i].find(*j) != a[i].end()) {
        st.erase(j);
        break;
      }
  if (st.size() == 0) {
    cout << "NO";
    return 0;
  }
  for (char i = 'a'; i <= 'z'; i++) {
    if (st.find(i) != st.end()) {
      if (DFS(i)) {
        cout << "NO";
        return 0;
      }
    }
  }
  for (auto i = sym.begin(); i != sym.end(); i++)
    if (s.find(*i) == string::npos) {
      cout << "NO";
      return 0;
    }
  cout << s;
  return 0;
}
int DFS(int v) {
  s += v;
  if (u[v] == 1) return 1;
  u[v] = 1;
  if (a[v].size() == 0) return 0;
  return DFS(*(a[v].begin()));
}
