···97979898Analyze your OASIS report and extrapolate the next value for each history. *What is the sum of these extrapolated values?*
9999100100-To begin, [get your puzzle input](9/input).
100100+Your puzzle answer was `1641934234`.
101101+102102+The first half of this puzzle is complete! It provides one gold star: \*
103103+104104+\--- Part Two ---
105105+----------
106106+107107+Of course, it would be nice to have *even more history* included in your report. Surely it's safe to just *extrapolate backwards* as well, right?
108108+109109+For each history, repeat the process of finding differences until the sequence of differences is entirely zero. Then, rather than adding a zero to the end and filling in the next values of each previous sequence, you should instead add a zero to the *beginning* of your sequence of zeroes, then fill in new *first* values for each previous sequence.
110110+111111+In particular, here is what the third example history looks like when extrapolating back in time:
112112+113113+```
114114+5 10 13 16 21 30 45
115115+ 5 3 3 5 9 15
116116+ -2 0 2 4 6
117117+ 2 2 2 2
118118+ 0 0 0
119119+120120+```
121121+122122+Adding the new values on the left side of each sequence from bottom to top eventually reveals the new left-most history value: `*5*`.
123123+124124+Doing this for the remaining example data above results in previous values of `*-3*` for the first history and `*0*` for the second history. Adding all three new values together produces `*2*`.
125125+126126+Analyze your OASIS report again, this time extrapolating the *previous* value for each history. *What is the sum of these extrapolated values?*
101127102128Answer:
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131131+132132+You can also [Shareon [Twitter](https://twitter.com/intent/tweet?text=I%27ve+completed+Part+One+of+%22Mirage+Maintenance%22+%2D+Day+9+%2D+Advent+of+Code+2023&url=https%3A%2F%2Fadventofcode%2Ecom%2F2023%2Fday%2F9&related=ericwastl&hashtags=AdventOfCode) [Mastodon](javascript:void(0);)] this puzzle.