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+Day 5: Binary Boarding
+You board your plane only to discover a new problem: you dropped your boarding
+pass! You aren't sure which seat is yours, and all of the flight attendants are
+busy with the flood of people that suddenly made it through passport control.
+You write a quick program to use your phone's camera to scan all of the nearby
+boarding passes (your puzzle input); perhaps you can find your seat through
+process of elimination.
+Instead of zones or groups, this airline uses binary space partitioning to seat
+people. A seat might be specified like FBFBBFFRLR, where F means "front", B
+means "back", L means "left", and R means "right".
+The first 7 characters will either be F or B; these specify exactly one of the
+128 rows on the plane (numbered 0 through 127). Each letter tells you which half
+of a region the given seat is in. Start with the whole list of rows; the first
+letter indicates whether the seat is in the front (0 through 63) or the back (64
+through 127). The next letter indicates which half of that region the seat is in,
+and so on until you're left with exactly one row.
+For example, consider just the first seven characters of FBFBBFFRLR:
+- Start by considering the whole range, rows 0 through 127.
+- F means to take the lower half, keeping rows 0 through 63.
+- B means to take the upper half, keeping rows 32 through 63.
+- F means to take the lower half, keeping rows 32 through 47.
+- B means to take the upper half, keeping rows 40 through 47.
+- B keeps rows 44 through 47.
+- F keeps rows 44 through 45.
+- The final F keeps the lower of the two, row 44.
+The last three characters will be either L or R; these specify exactly one of the
+8 columns of seats on the plane (numbered 0 through 7). The same process as above
+proceeds again, this time with only three steps. L means to keep the lower half,
+while R means to keep the upper half.
+For example, consider just the last 3 characters of FBFBBFFRLR:
+- Start by considering the whole range, columns 0 through 7.
+- R means to take the upper half, keeping columns 4 through 7.
+- L means to take the lower half, keeping columns 4 through 5.
+- The final R keeps the upper of the two, column 5.
+So, decoding FBFBBFFRLR reveals that it is the seat at row 44, column 5.
+Every seat also has a unique seat ID: multiply the row by 8, then add the column.
+In this example, the seat has ID 44 * 8 + 5 = 357.
+Here are some other boarding passes:
+- BFFFBBFRRR: row 70, column 7, seat ID 567.
+- FFFBBBFRRR: row 14, column 7, seat ID 119.
+- BBFFBBFRLL: row 102, column 4, seat ID 820.
+As a sanity check, look through your list of boarding passes. What is the highest
+seat ID on a boarding pass?
+Your puzzle answer was 970.
+The first half of this puzzle is complete! It provides one gold star: *