Subsequences Summing to Sevens

문제

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.

입력

The first line of input contains \(N\) (\(1 \leq N \leq 50,000\)). The next \(N\) lines each contain the \(N\) integer IDs of the cows (all are in the range \(0 \ldots 1,000,000\)).

출력

Please output the number of cows in the largest consecutive group whose IDs sum to a multiple of 7. If no such group exists, output 0.

You may want to note that the sum of the IDs of a large group of cows might be too large to fit into a standard 32-bit integer. If you are summing up large groups of IDs, you may therefore want to use a larger integer data type, like a 64-bit "long long" in C/C++.

힌트

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

7
3
5
1
6
2
14
10

5