Czechs to the West, Slovaks to the east

Would it be possible that after WW2 Czechoslovakia is not reformed but rather kept as two separate states, one going to western camp, other to the eastern.

Obviously there was little common CS identity but there was a history of living together.

While it was mostly liberated by Soviets Americans were there so "boots on the ground" rule could apply, specially if post-war division isn't completly worked out.

Thoughts?
 
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