#include <bits/stdc++.h>
using namespace std;
struct node {
  string ss;
  int len;
  bool operator<(node b) const { return len < b.len; }
} s[110];
bool kmp(string s1, string s2) {
  int l1 = s1.length();
  int l2 = s2.length();
  int next[110];
  int i, j;
  i = 0;
  j = -1;
  next[0] = -1;
  while (i < l2 && j < l2) {
    if (s2[i] == s2[j] || j == -1) {
      i++;
      j++;
      next[i] = j;
    } else
      j = next[j];
  }
  i = 0;
  j = 0;
  while (i < l1 && j < l2) {
    if (s1[i] == s2[j] || j == -1) {
      i++;
      j++;
    } else
      j = next[j];
  }
  if (j == l2)
    return 1;
  else
    return 0;
}
int main() {
  int i;
  int n;
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> s[i].ss;
    s[i].len = s[i].ss.length();
  }
  sort(s + 1, s + n + 1);
  int flag = 0;
  for (i = 2; i <= n; i++) {
    if (!kmp(s[i].ss, s[i - 1].ss)) flag = 1;
  }
  if (flag == 1) {
    cout << "NO";
    return 0;
  }
  if (flag == 0) cout << "YES" << endl;
  for (i = 1; i <= n; i++) cout << s[i].ss << endl;
  return 0;
}

### Prompt

Please create a solution in Cpp to the following problem:

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;
struct node {
  string ss;
  int len;
  bool operator<(node b) const { return len < b.len; }
} s[110];
bool kmp(string s1, string s2) {
  int l1 = s1.length();
  int l2 = s2.length();
  int next[110];
  int i, j;
  i = 0;
  j = -1;
  next[0] = -1;
  while (i < l2 && j < l2) {
    if (s2[i] == s2[j] || j == -1) {
      i++;
      j++;
      next[i] = j;
    } else
      j = next[j];
  }
  i = 0;
  j = 0;
  while (i < l1 && j < l2) {
    if (s1[i] == s2[j] || j == -1) {
      i++;
      j++;
    } else
      j = next[j];
  }
  if (j == l2)
    return 1;
  else
    return 0;
}
int main() {
  int i;
  int n;
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> s[i].ss;
    s[i].len = s[i].ss.length();
  }
  sort(s + 1, s + n + 1);
  int flag = 0;
  for (i = 2; i <= n; i++) {
    if (!kmp(s[i].ss, s[i - 1].ss)) flag = 1;
  }
  if (flag == 1) {
    cout << "NO";
    return 0;
  }
  if (flag == 0) cout << "YES" << endl;
  for (i = 1; i <= n; i++) cout << s[i].ss << endl;
  return 0;
}

```