--- 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
32*v**>**>**>*35*v*5623
32552456*v**>**>*54
3446585845*v*52
4546657867*v**>*6
14385987984*v*4
44578769877*v*6
36378779796*v**>*
465496798688*v*
456467998645*v*
12246868655*<**v*
25465488877*v*5
43226746555*v**>*

```

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?*