In a research facility, three security clearances are available: Alpha ($A$), Beta ($B$), and Gamma ($G$). We know that:

• $60\%$ of the staff have Alpha clearance.
• $50\%$ have Beta clearance.
• $40\%$ have Gamma clearance.
• Every staff member has at least one clearance.
• No one has both Alpha and Gamma clearances without also having Beta clearance (i.e., $A \cap G \subseteq B$).
• $10\%$ of the staff have all three clearances.

Determine the percentage of the staff that have exactly two clearances.