P is a positive decimal (base 10) integer consisting entirely of the digit 3, and Q is a positive decimal integer consisting entirely of the digit 7. In the base-10 expansion of P*Q, the digit 3 is repeated precisely three times and the digit 7 is repeated precisely seven times. The product P*Q may consist of other digits besides 3 and 7.

Given that N is the minimum value of P*Q, determine the remainder when N is divided by 37.

Note: Try to derive a non computer assisted method, although computer programs/spreadsheet solutions are welcome.