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.