Let $z$ and $w$ be complex numbers such that $|z + 1 + 3i| = 1$ and $|w - 7 - 8i| = 3.$  Find the smallest possible value of $|z - w|.$
Question:
Let $z$ and $w$ be complex numbers such that $|z + 1 + 3i| = 1$ and $|w - 7 - 8i| = 3.$  Find the smallest possible value of $|z - w|.$
Answer:
Let's think step by step.

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\sqrt{185} - 4
Let $z$ and $w$ be complex numbers such that $|z + 1 + 3i| = 1$ and $|w - 7 - 8i| = 3.$  Find the smallest possible value of $|z - w|.$
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