Problem Statement

You are given $N strings S_1,S_2,\dots,S_N$ consisting of lowercase English alphabets.
Consider choosing some number of strings from $S_1,S_2,\dots,S_N$.
Find the maximum number of distinct alphabets that satisfy the following condition: "the alphabet is contained in exactly K of the chosen strings."

Input

Input is given from Standard Input in the following format:
N K
S_1
S_2
$\vdots$
S_N

Output

Print the answer.

Constraints

• $1 \le N \le 15$
• $1 \le K \le N$
• N and K are integers.
• S_i is a non-empty string consisting of lowercase English alphabets.
• For each integer i such that $1 \le i \le N, S_i$ does not contain two or more same alphabets.
• If $i \neq j$, then $S_i \neq S_j$.

Sample Input 1

4 2
abi
aef
bc
acg

Sample Output 1

3

When S_1,S_3, and S_4 are chosen, a,b, and c occur in exactly two of the strings.
There is no way to choose strings so that 4 or more alphabets occur in exactly 2 of the strings, so the answer is 3.

Sample Input 2

2 2
a
b

Sample Output 2

0

You cannot choose the same string more than once.

Sample Input 3

5 2
abpqxyz
az
pq
bc
cy

Sample Output 3

7

见题面 Input 部分

见题面 Output 部分