#include <bits/stdc++.h>
using namespace std;
const long long INF = 1000000007;
const int MAX_N = 200;
string s[MAX_N];
int chek(string a, string b) {
  for (int i = 0; i < b.size(); i++) {
    int q = 1;
    for (int j = 0; j < a.size(); j++) {
      if (b[i + j] != a[j]) {
        q = 0;
        break;
      }
    }
    if (q == 1) return 1;
  }
  return 0;
}
int g[MAX_N][MAX_N];
int cnt[MAX_N];
int flag[MAX_N];
vector<string> ans;
int main() {
  int n, a;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> s[i];
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      g[i][j] = chek(s[i], s[j]);
      g[j][i] = chek(s[j], s[i]);
      if (g[i][j] + g[j][i] == 0) {
        cout << "NO";
        return 0;
      }
    }
  }
  for (int k = n - 1; k >= 0; k--) {
    a = -1;
    for (int j = 0; j < n; j++) {
      int q = 0;
      for (int i = 0; i < n; i++) {
        if (i != j && flag[i] == 0) {
          q += g[i][j];
        }
      }
      if (q == k) {
        a = j;
        break;
      }
    }
    ans.push_back(s[a]);
    flag[a] = 1;
  }
  reverse(ans.begin(), ans.end());
  if (ans.size() == n) {
    cout << "YES" << endl;
    for (int i = 0; i < n; i++) cout << ans[i] << endl;
    return 0;
  }
  cout << "NO";
  return 0;
}

### 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 INF = 1000000007;
const int MAX_N = 200;
string s[MAX_N];
int chek(string a, string b) {
  for (int i = 0; i < b.size(); i++) {
    int q = 1;
    for (int j = 0; j < a.size(); j++) {
      if (b[i + j] != a[j]) {
        q = 0;
        break;
      }
    }
    if (q == 1) return 1;
  }
  return 0;
}
int g[MAX_N][MAX_N];
int cnt[MAX_N];
int flag[MAX_N];
vector<string> ans;
int main() {
  int n, a;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> s[i];
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      g[i][j] = chek(s[i], s[j]);
      g[j][i] = chek(s[j], s[i]);
      if (g[i][j] + g[j][i] == 0) {
        cout << "NO";
        return 0;
      }
    }
  }
  for (int k = n - 1; k >= 0; k--) {
    a = -1;
    for (int j = 0; j < n; j++) {
      int q = 0;
      for (int i = 0; i < n; i++) {
        if (i != j && flag[i] == 0) {
          q += g[i][j];
        }
      }
      if (q == k) {
        a = j;
        break;
      }
    }
    ans.push_back(s[a]);
    flag[a] = 1;
  }
  reverse(ans.begin(), ans.end());
  if (ans.size() == n) {
    cout << "YES" << endl;
    for (int i = 0; i < n; i++) cout << ans[i] << endl;
    return 0;
  }
  cout << "NO";
  return 0;
}

```