--- SOS GPS ---

Hey fellow,

🎅 Santa needs your help once again to save this festive moment 🎄

With the world population officially hitting 8 billion people, Santa's job isn't getting easier. Enter the ✨Gift-o-tron-3000✨.

Santa could already see it! Using all the saved time to enjoy more cookies and a few extra glasses of milk left by the kids! The perfect Christmas all around... Or so it should have been.

Unfortunately, the shady elf merchant of this machine "forgot" to mention that the Gift Positioning System (GPS) of the machine significantly slows down with the number of kids increasing.

Luckily, we can provide our own GPS algorithm to the Gift-o-tron-3000! Lucky indeed, you know your way around code. They don't call you the sharpest coder of the North Pole for nothing! All the kids of the world and Santa themself are counting on you! Let operation SOS GPS begin ✨

The kids' address list looks as follows:

tamo - RLRLR
loic - RLLL
kero - LRLR
luna - LRRR
caro - LRL
lena - RLLR
thomas - LRLL
tommy - LLL
chayaline - LRLL

On the left is the kid's name that needs to get their gift. On the right is the path from Santa's home to the kid's house. An L means Santa needs to turn left, and an R means they need to turn right. For example, for Santa to go to luna's house, they need to turn left, right, right, and right.

Unfortunately (again), Rudolph has a bad left foot. We need to prioritize turning left before they run out of steam. With the input above, our new GPS map must look like this:

          LL - - - - - - tommy
          /   L - - - -  chayaline, thomas
         /   /
        /   L - - - - -  caro
       /   / \
      /   /   R - - - -  kero
     L - R - RR - - - -  luna
    /
   /      L - - - - - -  loic
  o      /
   \    L - R - - - - -  lena
    \  /
     RL - RLR - - - - -  tamo
  

Notice how some nodes are collapsed together? That's the important part; it will define how many stops Santa's reindeer needs to make. Basically, one per node.

Your goal is to find which kid Santa can get to with as few stops as possible and gives his name.

In the above case, tommy and tamo are the only kids accessible in two instructions. But since tommy appears first in the structure, he gets his gift first.

To determine who is first in the structure, you must use the lexicographical comparison between their path. In this case, LLL appears before RLRLR. In case a path is a subset of another, the shorter wins.

BRAVO!

--- Part2 ---

You are able to find the closest kids! But what about the others? The old GPS became so slow that we would not have been able to deliver all the gifts on time!

Now, you need to count how many stops it'll take Santa to go from the closest to the next closest kid until there are no kids remaining. Even kids in Antarctica must receive their well deserved gifts!

You need to find how many stops Santa will make. The number of stops will help Santa know how many carrots they needs to bring for their beloved reindeers.

Step 0: We're at Santa house.

           LL - - - - -  tommy
          /   L - - - -  chayaline, thomas
         /   /
        /   L - - - - -  caro
       /   / \
      /   /   R - - - -  kero
     L - R - RR - - - -  luna
    /
   /      L - - - - - -  loic
  o      /
   \    L - R - - - - -  lena
    \  /
     RL - RLR - - - - -  tamo

Step 1: tommy is the closest, 2 stops away.

           LL - - - - -  2 stops in total
          /   L - - - -  chayaline, thomas
         /   /
        /   L - - - - -  caro
       /   / \
      /   /   R - - - -  kero
     L - R - RR - - - -  luna
    /
   /      L - - - - - -  loic
  o      /
   \    L - R - - - - -  lena
    \  /
     RL - RLR - - - - -  tamo

Step 2: caro is the closest, 3 stops away.

              L - - - -  chayaline, thomas
             /
            L - - - - -  5 stops in total
           / \
          /   R - - - -  kero
     L - R - RR - - - -  luna
    /
   /      L - - - - - -  loic
  o      /
   \    L - R - - - - -  lena
    \  /
     RL - RLR - - - - -  tamo

Step 3: chayaline and thomas are the closest, 1 stops away.

              L  - - - - 6 stops in total
             /
            L
           / \
          /   R - - - -  kero
     L - R - RR - - - -  luna
    /
   /      L - - - - - -  loic
  o      /
   \    L - R - - - - -  lena
    \  /
     RL - RLR - - - - -  tamo

Step 4: kero is the closest, 2 stops away.

            L
           / \
          /   R - - - -  8 stops in total
     L - R - RR - - - -  luna
    /
   /      L - - - - - -  loic
  o      /
   \    L - R - - - - -  lena
    \  /
     RL - RLR - - - - -  tamo


Step 5: luna is the closest, 3 stops away.

     L - R - RR - - - -  11 stops in total
    /
   /      L - - - - - -  loic
  o      /
   \    L - R - - - - -  lena
    \  /
     RL - RLR - - - - -  tamo

Step 6: tamo is the closest, 5 stops away.

          L - - - - - -  loic
  o      /
   \    L - R - - - - -  lena
    \  /
     RL - RLR - - - - -  16 stops in total

Step 7: loic is the closest, 3 stops away.

          L - - - - - -  19 stops in total
  o      /
   \    L - R - - - - -  lena
    \  /
     RL


Step 8: lena is the closest, 2 stops away.

  o
   \    L - R - - - - -  21 stops in total
    \  /
     RL

In the example above, we have 21 stops in total.

Don't forget: If two kids are at the same distance, you still need to deliver your gift to the kid that's first, in the lexicographical order from the point of view of Santa's house.

TURBO BRAVO²!