William is facilitating a get-together for n of his broker companions. They began a conversation on different monetary forms they exchange, however there's an issue: not all of his dealer companions like each cash. They like a few monetary standards, yet not others. For each William's companion I it is known whether he enjoys
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William is facilitating a get-together for n of his broker companions. They began a conversation on different monetary forms they exchange, however there's an issue: not all of his dealer companions like each cash. They like a few monetary standards, yet not others.
For each William's companion I it is known whether he enjoys money j. There are m monetary standards altogether. It is likewise realized that a merchant dislike more than p monetary forms.
Since companions need to have some normal subject for conversations they need to track down the biggest via cardinality (perhaps vacant) subset of monetary standards, with the end goal that there are essentially ⌈n2⌉ companions (gathered together) who like every money in this subset.
Input
The primary line contains three integers n,m and p (1≤n≤2⋅105,1≤p≤m≤60,1≤p≤15), which is the number of broker companions, the number of monetary forms, the greatest number of monetary standards every companion can like.
Every one of the following n lines contain m characters. The j-th character of I-th line is 1 if companion I prefers the cash j and 0 in any case. It is ensured that the number of ones in each line doesn't surpass p.
Output
Print a line of length m, which characterizes the subset of monetary forms of the greatest size, which are loved by to some degree half, everything being equal. Monetary forms having a place with this subset should be implied by the character 1.
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