2013 2013 Times

Consider \(N=20132013 \ldots 2013 \), where \(N\) consists of the number 2013 concatenated (repeated) 2013 times. What is the remainder of N when divided by 1001?

Details and assumptions

Concatenated: Combining 2 strings of numbers into one, by placing the first string directly before the second. For example, the number 123 concatenated 4 times would be 123123123123.

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