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Triangle A intersects with Triangle B and shares a common area of \(30 \text{ m}^2\). Triangle B shares a common area of \(40\text{ m}^2\) with Triangle C, and Triangle C shares a common area of \(50 \text{ m}^2\) with Triangle A. If all triangles have integer areas not greater than \(60 \text{ m}^2\), and that every triangle must have an area strictly of its own, what is the minimum sum of areas of the three triangles?

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