Problem
2025 AIME II Problem 3
Four unit squares form a 2 \times 2 grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. One example is shown below (red is solid, blue is dashed). Find the number of such colorings.
![[asy] size(4cm); defaultpen(linewidth(1.2)); draw((0, 0) -- (2, 0) -- (2, 1), red); draw((0, 1) -- (1, 1) -- (1, 2) -- (2,2), red); draw((0, 0) -- (0, 1),blue+dotted); draw((1, 0) -- (1, 1) -- (2, 1) -- (2, 2),blue+dotted); draw((0, 1) -- (0, 2) -- (1, 2),blue+dotted); [/asy]](/static/aops/1a7f9f0169c01de562e7c231be7e7e6f020c65ae.png)
Leading zeroes must be inputted, so if your answer is 34, then input 034
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