chromatic number in directed graphs

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the chromatic number in directed graphs $χ_A$(D) is defined as the smallest integer such that there is a coloration without monochromatic directed cycles. it follows that if D is a planar graph, then: $χ_A$(D) ≤ 3. I have to prove: Show that if $D$ is a planar directed graph without directed edges going in both ways, then $χ_A$ (D) ≤ 3 I dont have any idea of how to start, This is a question for my final exam but i dont what to do