There are $n$ strings $s_1, s_2,\ ..., s_n$ of length $m$ and a set of strings $S$.
Here, $f(str, S)$ denotes the numbers of substrings of $str$ that are in $S$. For example, $f(aab, \{a, ab\}) = 3$.
Note: $str$ is a string in $f(str, S)$

Now, you have removed $S$ and you are given $s_1, s_2,\ ..., s_n$ and $f(s_1, S), f(s_2, S),\ ..., f(s_n, S)$. Find a set of string $S'$ that maximizes the following score formula:

$score\ of\ test = (1- \frac{tan^{-1}(\sqrt{\sum (f(s_i, S) - f(s_i, S'))^2})}{\pi/2}) \times 5$

There are $20$ tests for this problem.

Input format

• The first line contains two integers $n$ and $m$.
  $1 \leq n, m \leq 64$
• Each of following $n$ lines contains a string $s_i$ and an integer $f(s_i, S)$.
  $1 \leq f(s_i, S) \leq 500$
  Length of $s_i$ is $m$

Output format

In the first line, print $sz$ that is the size of $S'$ and in the following $sz$ lines, print each $S'$'s element in any order.

The following conditions must be satisfied:

• $1 \leq sz \leq 128$
• $1 \leq each\ S'\ element\ length \leq m$
• All elements must be unique.

It is guaranteed that $S$ satisfies the mentioned conditions.