part2 (3485B)
1--- Part Two --- 2 3Once you give them the coordinates, the Elves quickly deploy an Instant Monitoring Station to the 4location and discover the worst: there are simply too many asteroids. 5 6The only solution is [1m[97mcomplete vaporization by giant laser[0m. 7 8Fortunately, in addition to an asteroid scanner, the new monitoring station also comes equipped with 9a giant rotating laser perfect for vaporizing asteroids. The laser starts by pointing 10[1m[97mup[0m and always rotates [1m[97mclockwise[0m, vaporizing any asteroid it hits. 11 12If multiple asteroids are [1m[97mexactly[0m in line with the station, the laser only has enough power to 13vaporize [1m[97mone[0m of them before continuing its rotation. In other words, the same asteroids that can be 14[1m[97mdetected[0m can be vaporized, but if vaporizing one asteroid makes another one detectable, the 15newly-detected asteroid won't be vaporized until the laser has returned to the same position by 16rotating a full 360 degrees. 17 18For example, consider the following map, where the asteroid with the new monitoring station (and 19laser) is marked X: 20 21.#....#####...#.. 22##...##.#####..## 23##...#...#.#####. 24..#.....X...###.. 25..#.#.....#....## 26 27The first nine asteroids to get vaporized, in order, would be: 28 29.#....###[1m[97m2[0m[1m[97m4[0m...#.. 30##...##.[1m[97m1[0m[1m[97m3[0m#[1m[97m6[0m[1m[97m7[0m..[1m[97m9[0m# 31##...#...[1m[97m5[0m.[1m[97m8[0m####. 32..#.....X...###.. 33..#.#.....#....## 34 35Note that some asteroids (the ones behind the asteroids marked 1, 5, and 7) won't have a chance to 36be vaporized until the next full rotation. The laser continues rotating; the next nine to be 37vaporized are: 38 39.#....###.....#.. 40##...##...#.....# 41##...#......[1m[97m1[0m[1m[97m2[0m[1m[97m3[0m[1m[97m4[0m. 42..#.....X...[1m[97m5[0m##.. 43..#.[1m[97m9[0m.....[1m[97m8[0m....[1m[97m7[0m[1m[97m6[0m 44 45The next nine to be vaporized are then: 46 47.[1m[97m8[0m....###.....#.. 48[1m[97m5[0m[1m[97m6[0m...[1m[97m9[0m#...#.....# 49[1m[97m3[0m[1m[97m4[0m...[1m[97m7[0m........... 50..[1m[97m2[0m.....X....##.. 51..[1m[97m1[0m.............. 52 53Finally, the laser completes its first full rotation (1 through 3), a second rotation (4 through 8), 54and vaporizes the last asteroid (9) partway through its third rotation: 55 56......[1m[97m2[0m[1m[97m3[0m[1m[97m4[0m.....[1m[97m6[0m.. 57......[1m[97m1[0m...[1m[97m5[0m.....[1m[97m7[0m 58................. 59........X....[1m[97m8[0m[1m[97m9[0m.. 60................. 61 62In the large example above (the one with the best monitoring station location at 11,13): 63 64 65 - The 1st asteroid to be vaporized is at 11,12. 66 67 - The 2nd asteroid to be vaporized is at 12,1. 68 69 - The 3rd asteroid to be vaporized is at 12,2. 70 71 - The 10th asteroid to be vaporized is at 12,8. 72 73 - The 20th asteroid to be vaporized is at 16,0. 74 75 - The 50th asteroid to be vaporized is at 16,9. 76 77 - The 100th asteroid to be vaporized is at 10,16. 78 79 - The 199th asteroid to be vaporized is at 9,6. 80 81 - [1m[97mThe 200th asteroid to be vaporized is at 8,2.[0m 82 83 - The 201st asteroid to be vaporized is at 10,9. 84 85 - The 299th and final asteroid to be vaporized is at 11,1. 86 87 88The Elves are placing bets on which will be the [1m[97m200th[0m asteroid to be vaporized. Win the bet by 89determining which asteroid that will be; [1m[97mwhat do you get if you multiply its X coordinate by 100 and 90then add its Y coordinate?[0m (For example, 8,2 becomes [1m[97m802[0m.) 91 92