## \-\-\- Day 17: Clumsy Crucible --- The lava starts flowing rapidly once the Lava Production Facility is operational. As you leave, the reindeer offers you a parachute, allowing you to quickly reach Gear Island. As you descend, your bird's-eye view of Gear Island reveals why you had trouble finding anyone on your way up: half of Gear Island is empty, but the half below you is a giant factory city! You land near the gradually-filling pool of lava at the base of your new _lavafall_. Lavaducts will eventually carry the lava throughout the city, but to make use of it immediately, Elves are loading it into large [crucibles](https://en.wikipedia.org/wiki/Crucible) on wheels. The crucibles are top-heavy and pushed by hand. Unfortunately, the crucibles become very difficult to steer at high speeds, and so it can be hard to go in a straight line for very long. To get Desert Island the machine parts it needs as soon as possible, you'll need to find the best way to get the crucible _from the lava pool to the machine parts factory_. To do this, you need to minimize _heat loss_ while choosing a route that doesn't require the crucible to go in a _straight line_ for too long. Fortunately, the Elves here have a map (your puzzle input) that uses traffic patterns, ambient temperature, and hundreds of other parameters to calculate exactly how much heat loss can be expected for a crucible entering any particular city block. For example: ``` 2413432311323 3215453535623 3255245654254 3446585845452 4546657867536 1438598798454 4457876987766 3637877979653 4654967986887 4564679986453 1224686865563 2546548887735 4322674655533 ``` Each city block is marked by a single digit that represents the _amount of heat loss if the crucible enters that block_. The starting point, the lava pool, is the top-left city block; the destination, the machine parts factory, is the bottom-right city block. (Because you already start in the top-left block, you don't incur that block's heat loss unless you leave that block and then return to it.) Because it is difficult to keep the top-heavy crucible going in a straight line for very long, it can move _at most three blocks_ in a single direction before it must turn 90 degrees left or right. The crucible also can't reverse direction; after entering each city block, it may only turn left, continue straight, or turn right. One way to _minimize heat loss_ is this path: ``` 2>>34^>>>1323 32v>>>35v5623 32552456v>>54 3446585845v52 4546657867v>6 14385987984v4 44578769877v6 36378779796v> 465496798688v 456467998645v 12246868655 ``` This path never moves more than three consecutive blocks in the same direction and incurs a heat loss of only `102`. Directing the crucible from the lava pool to the machine parts factory, but not moving more than three consecutive blocks in the same direction, _what is the least heat loss it can incur?_