#include <bits/stdc++.h>
using namespace std;
void prefix(string pat, int Pi[]) {
  Pi[0] = 0;
  int i = 1, j = 0;
  int sz = pat.size();
  while (i < sz) {
    if (pat[i] == pat[j])
      Pi[i++] = ++j;
    else if (j == 0)
      Pi[i++] = 0;
    else
      j = Pi[j - 1];
  }
}
bool KMP(string pattern, string target) {
  int n = target.length(), m = pattern.length(), i = 0, j = 0, rest;
  int Pi[m];
  prefix(pattern, Pi);
  while (i < n) {
    if (target[i] == pattern[j]) {
      i++, j++;
      if (j == m) {
        return 1;
      }
    } else if (j)
      j = Pi[j - 1];
    else
      i++;
  }
  return 0;
}
int main() {
  string pattern, target;
  vector<pair<int, string>> vp;
  int n;
  cin >> n;
  int a;
  string s;
  for (int i = 0; i < n; i++) {
    cin >> s;
    a = s.size();
    vp.push_back(make_pair(a, s));
  }
  sort(vp.begin(), vp.end());
  for (int i = 0; i < n - 1; i++) {
    pattern = vp[i].second;
    target = vp[i + 1].second;
    if (!KMP(pattern, target)) {
      cout << "NO" << endl;
      return 0;
    }
  }
  cout << "YES" << endl;
  for (int i = 0; i < n; i++) {
    cout << vp[i].second << endl;
  }
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

You are given n strings. Each string consists of lowercase English letters. Rearrange (reorder) the given strings in such a way that for every string, all strings that are placed before it are its substrings.

String a is a substring of string b if it is possible to choose several consecutive letters in b in such a way that they form a. For example, string "for" is contained as a substring in strings "codeforces", "for" and "therefore", but is not contained as a substring in strings "four", "fofo" and "rof".

Input

The first line contains an integer n (1 ≤ n ≤ 100) — the number of strings.

The next n lines contain the given strings. The number of letters in each string is from 1 to 100, inclusive. Each string consists of lowercase English letters.

Some strings might be equal.

Output

If it is impossible to reorder n given strings in required order, print "NO" (without quotes).

Otherwise print "YES" (without quotes) and n given strings in required order.

Examples

Input

5
a
aba
abacaba
ba
aba


Output

YES
a
ba
aba
aba
abacaba


Input

5
a
abacaba
ba
aba
abab


Output

NO


Input

3
qwerty
qwerty
qwerty


Output

YES
qwerty
qwerty
qwerty

Note

In the second example you cannot reorder the strings because the string "abab" is not a substring of the string "abacaba".

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
void prefix(string pat, int Pi[]) {
  Pi[0] = 0;
  int i = 1, j = 0;
  int sz = pat.size();
  while (i < sz) {
    if (pat[i] == pat[j])
      Pi[i++] = ++j;
    else if (j == 0)
      Pi[i++] = 0;
    else
      j = Pi[j - 1];
  }
}
bool KMP(string pattern, string target) {
  int n = target.length(), m = pattern.length(), i = 0, j = 0, rest;
  int Pi[m];
  prefix(pattern, Pi);
  while (i < n) {
    if (target[i] == pattern[j]) {
      i++, j++;
      if (j == m) {
        return 1;
      }
    } else if (j)
      j = Pi[j - 1];
    else
      i++;
  }
  return 0;
}
int main() {
  string pattern, target;
  vector<pair<int, string>> vp;
  int n;
  cin >> n;
  int a;
  string s;
  for (int i = 0; i < n; i++) {
    cin >> s;
    a = s.size();
    vp.push_back(make_pair(a, s));
  }
  sort(vp.begin(), vp.end());
  for (int i = 0; i < n - 1; i++) {
    pattern = vp[i].second;
    target = vp[i + 1].second;
    if (!KMP(pattern, target)) {
      cout << "NO" << endl;
      return 0;
    }
  }
  cout << "YES" << endl;
  for (int i = 0; i < n; i++) {
    cout << vp[i].second << endl;
  }
}

```