2026 Fermat Problem 22

A rectangle with height 20 cm and width 26 cm is painted with n vertical strips and n horizontal strips. Each vertical strip has height 20 cm and width 2 cm. Each horizontal strip has height 2 cm and width 26 cm. Each vertical strip overlaps each horizontal strip. Vertical strips do not overlap one another, and horizontal strips do not overlap one another. The area of the painted portion of the rectangle is \frac{12}{13} of the area of the rectangle. What is the value of n?

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