#include <bits/stdc++.h>
using namespace std;
const long long NMAX = 2e5 + 5, INF = 1e15 + 7, END = 1e5;
vector<int> z_function(string s) {
  int n = s.size();
  vector<int> z(n);
  z[0] = 0;
  for (int i = 1, l = 0, r = 0; i < n; ++i) {
    if (i <= r) z[i] = min(z[i - l], r - i + 1);
    while (i + z[i] < n && s[z[i]] == s[i + z[i]]) ++z[i];
    if (i + z[i] - 1 > r) {
      l = i;
      r = i + z[i] - 1;
    }
  }
  return z;
}
bool cmp(string s1, string s2) {
  string s = s1 + "#" + s2;
  vector<int> z = z_function(s);
  for (int i = s1.size(); i < s.size(); ++i)
    if (z[i] >= s1.size()) return true;
  return false;
}
vector<string> s;
int main() {
  int n;
  cin >> n;
  s.resize(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)
      if (cmp(s[j], s[i])) swap(s[j], s[i]);
  for (int i = 1; i < n; ++i)
    if (!cmp(s[i - 1], s[i])) return cout << "NO", 0;
  cout << "YES\n";
  for (int i = 0; i < n; ++i) cout << s[i] << "\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 NMAX = 2e5 + 5, INF = 1e15 + 7, END = 1e5;
vector<int> z_function(string s) {
  int n = s.size();
  vector<int> z(n);
  z[0] = 0;
  for (int i = 1, l = 0, r = 0; i < n; ++i) {
    if (i <= r) z[i] = min(z[i - l], r - i + 1);
    while (i + z[i] < n && s[z[i]] == s[i + z[i]]) ++z[i];
    if (i + z[i] - 1 > r) {
      l = i;
      r = i + z[i] - 1;
    }
  }
  return z;
}
bool cmp(string s1, string s2) {
  string s = s1 + "#" + s2;
  vector<int> z = z_function(s);
  for (int i = s1.size(); i < s.size(); ++i)
    if (z[i] >= s1.size()) return true;
  return false;
}
vector<string> s;
int main() {
  int n;
  cin >> n;
  s.resize(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)
      if (cmp(s[j], s[i])) swap(s[j], s[i]);
  for (int i = 1; i < n; ++i)
    if (!cmp(s[i - 1], s[i])) return cout << "NO", 0;
  cout << "YES\n";
  for (int i = 0; i < n; ++i) cout << s[i] << "\n";
}

```