We have a list of $$$N$$$ strings $$$S_i$$$. All strings have length $$$M$$$ and consist only of characters A, B, C and D. Let us define the distance between two strings $$$X$$$ and $$$Y$$$ as the number of indices $$$j$$$, where the strings have different characters ($$$X_j \neq Y_j$$$). We know that the list of strings $$$S_i$$$ contains precisely one special string that has distance $$$K$$$ to all other strings. Note that there might be other pairs of strings with a distance of $$$K$$$. We are experiencing problems finding this special string, so please write a program to help us out.
The first line contains space-separated integers $$$N$$$, $$$M$$$ and $$$K$$$. Strings $$$S_i$$$ are given in the following $$$N$$$ lines.
Input limits
Output the index $$$i$$$ of the special string. Strings are numbered from $$$1$$$ to $$$N$$$ as given in the input.
5 10 2 DCDDDCCADA ACADDCCADA DBADDCCBDC DBADDCCADA ABADDCCADC
4
4 6 5 AABAAA BAABBB ABAAAA ABBAAB
2
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