Problem Statement

Let $S$ be a string consisting of lowercase English letters and $T$ be a string consisting of lowercase English letters and ?.
$S$ is said to be obtainable from $T$ when one can replace each occurrence of ? in $T$ with some lowercase English letter so that $T$ equals $S$.

For example, abcd and addd are obtainable from a??d, while bcdd is not.

You are given $N$ strings $S_1, S_2, \ldots, S_N$ consisting of lowercase English letters.
All of these strings have a length of $L$: $|S_1| = |S_2| = \cdots = |S_N| = L$.

A string $T$ of length $L$ consisting of lowercase English letters is arbitrarily chosen so that it contains exactly $K$ ?s.
Find the maximum possible number of strings among $S_1, S_2, \ldots, S_N$ that are obtainable from $T$.

Constraints

• $1 \leq N \leq 1000$
• $1 \leq L \leq 10$
• $0 \leq K \leq L$
• $N$, $L$, and $K$ are integers.
• Each of $S_1, S_2, \ldots, S_N$ is a string of length $L$ consisting of lowercase English letters.
• $S_1, S_2, \ldots, S_N$ are distinct.

Sample Input 1Copy

5 4 2
aabc
bbaa
abbc
cccc
acba

Sample Output 1Copy

3

If we let $T =$ a?b?, then $S_1 =$ aabc, $S_3 =$ abbc, and $S_5 =$ acba are obtainable from $T$. Here, three of the strings $S_1, S_2, \ldots, S_N$ are obtainable from $T$, which is the maximum possible number. Note that $K = 2$, so $T$ must be chosen to contain exactly two ?s.

Sample Input 2Copy

5 4 4
aabc
bbaa
abbc
cccc
acba

Sample Output 2Copy

5

If we let $T =$ ????, all of $S_1, S_2, S_3, S_4, S_5$ are obtainable from $T$.

Sample Input 3Copy

5 4 0
aabc
bbaa
abbc
cccc
acba

Sample Output 3Copy

1