# Problem K

Central String

You have a collection of strings of the same length $L$ and are wondering how similar they are. We can say that the distance $d(S,T)$ between two strings $S$ and $T$ of the same length is the number of indices $i$ where $S_ i \neq T_ i$. For example, $d(\texttt{berry}, \texttt{bears}) = 2$ since only the third and fifth characters differ.

You wonder if your strings are very close to each other.
That is, for a given distance $D$ you have in mind, is there a
string $S$ of length
$L$ such that $d(S,A) \leq D$ for each string
$A$ in your collection?
Call such a string $S$ a
*central string*. Note that a central string does not
necessarily have to be one of your strings.

## Input

The first line of input contains three integers $N$ ($1 \leq N \leq 50$), $L$ ($1 \leq L \leq 1\, 000\, 000$), and $D$ ($0 \leq D \leq 6$). Here, $N$ indicates the number of strings in your collection, $L$ is the common length of these strings, and $D$ is the distance bound you are curious about. Then $N$ lines follow, the $i$’th such line contains a single string $A_ i$ of length $L$ consisting of only lowercase letters.

You are further guaranteed that $N \cdot L \leq 1\, 000\, 000$.

## Output

Output consists of a single line. If there is a string
$S$ consisting of only
lowercase letters such that $d(S,A_ i) \leq D$ for each
$1 \leq i \leq N$, output
any such string. Otherwise, simply output the single digit
`0` to indicate there is no central
string.

Sample Input 1 | Sample Output 1 |
---|---|

2 4 1 abba bbca |
abca |

Sample Input 2 | Sample Output 2 |
---|---|

3 4 3 abcd efgh ijkl |
abgl |

Sample Input 3 | Sample Output 3 |
---|---|

3 4 2 abcd efgh ijkl |
0 |