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Since each garden is connected to at most 3 gardens, there's always an available color for each garden. For example, if one garden is next to gardens with colors 1, 3, 4, then color #2 is available.
Calculate the final vector of how the robot travels after executing all instructions once - it consists of a change in position plus a change in direction.
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<summary>Hint 2</summary>
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The robot stays in the circle iff (looking at the final vector) it changes direction (ie. doesn't stay pointing north), or it moves 0.
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