Suppose a lecture hall has a rectangular array of chairs with \(r\) rows and \(c\) columns. Suppose further that there are precisely \(19\) girls seated in each row and precisely \(15\) boys seated in each column.
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If exactly \(14\) chairs are empty then find the minimum possible value of \(r \times c.\)

**Details and Assumptions**:

- A maximum of one person per chair is allowed.

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