Three people $A, B,$ and $C$ are sitting on stairs one after another such that $C$ on the first stair cannot see the two above him and $B$ on the second stair cannot see the one above him. There are 2 red and 2 white hats available and each person is wearing one of them. However, no one knows the color of their hat.

The following conversation then took place between $A$ and $B$:

$A:$ I don't know which color hat I'm wearing.

$B:$ At first I didn't know, but I know the color of my hat now.

If $C$ is wearing a red colored hat, what color hat is $B$ wearing?

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