Brain Teaser: Twisted Wires

Given: six boxes - represented by the enclosed regions A, B and C below.

Is it possible to connect box A to A, B to B, and C to C with lines which do not cross, touch each other, or go outside the surrounding frame? The lines may be curvy, but may not go through the boxes or along the border of the surrounding frame.

Puzzle by Cliff Pickover
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