Must be a popular lecturer

Suppose a lecture hall has a rectangular array of chairs with rr rows and cc columns. Suppose further that there are precisely 1919 girls seated in each row and precisely 1515 boys seated in each column.

If exactly 1414 chairs are empty then find the minimum possible value of r×c.r \times c.

Details and Assumptions:

  • A maximum of one person per chair is allowed.
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