P3131 [USACO16JAN] Subsequences Summing to Sevens S

Farmer John's $N$ cows are standing in a row, as they have a tendency to do from time to time. Each cow is labeled with a distinct integer ID number so FJ can tell them apart. FJ would like to take a photo of a contiguous group of cows but, due to a traumatic childhood incident involving the numbers $1 \ldots 6$, he only wants to take a picture of a group of cows if their IDs add up to a multiple of 7. Please help FJ determine the size of the largest group he can photograph.

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In this example, $5+1+6+2+14 = 28$.