In Pascal's Triangle, each number is the sum of the number just above it and to the left and the number just above it and to the right. A number in Pascal's Triangle is said to be divisible by 3 if it leaves a remainder of 0 when divided by 3. How many numbers in Row 12 of Pascal's Triangle are divisible by 3? Let's think step by step and output the final answer within \boxed{}.
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