#include <bits/stdc++.h>
using namespace std;
const long long MaxN = 302;
long long n;
string v[MaxN];
set<string> S[MaxN];
pair<long long, string> resp[MaxN];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> v[i];
    for (int j = 0; j < v[i].size(); j++) {
      string aux = "";
      for (int k = j; k < v[i].size(); k++) {
        aux += v[i][k];
        S[i].insert(aux);
      }
    }
  }
  for (int i = 0; i < n; i++) {
    int c = 0;
    for (int j = 0; j < n; j++) {
      if (i != j) {
        if (S[j].find(v[i]) != S[j].end()) {
          c++;
        }
      }
    }
    resp[i] = make_pair(c, v[i]);
  }
  sort(resp, resp + n);
  for (int i = 0; i < n; i++) {
    if (resp[i].first < i) {
      cout << "NO\n";
      return 0;
    }
  }
  cout << "YES\n";
  for (int i = n - 1; i >= 0; i--) {
    cout << resp[i].second << "\n";
  }
}

### 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;
const long long MaxN = 302;
long long n;
string v[MaxN];
set<string> S[MaxN];
pair<long long, string> resp[MaxN];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> v[i];
    for (int j = 0; j < v[i].size(); j++) {
      string aux = "";
      for (int k = j; k < v[i].size(); k++) {
        aux += v[i][k];
        S[i].insert(aux);
      }
    }
  }
  for (int i = 0; i < n; i++) {
    int c = 0;
    for (int j = 0; j < n; j++) {
      if (i != j) {
        if (S[j].find(v[i]) != S[j].end()) {
          c++;
        }
      }
    }
    resp[i] = make_pair(c, v[i]);
  }
  sort(resp, resp + n);
  for (int i = 0; i < n; i++) {
    if (resp[i].first < i) {
      cout << "NO\n";
      return 0;
    }
  }
  cout << "YES\n";
  for (int i = n - 1; i >= 0; i--) {
    cout << resp[i].second << "\n";
  }
}

```