## --- Day 21: Dirac Dice ---

There's not much to do as you slowly descend to the bottom of the ocean. The submarine computer challenges you to a nice game of *Dirac Dice*.

This game consists of a single die, two pawns, and a game board with a circular track containing ten spaces marked `1`

through `10`

clockwise. Each player's *starting space* is chosen randomly (your puzzle input). Player 1 goes first.

Players take turns moving. On each player's turn, the player rolls the die *three times* and adds up the results. Then, the player moves their pawn that many times *forward* around the track (that is, moving clockwise on spaces in order of increasing value, wrapping back around to `1`

after `10`

). So, if a player is on space `7`

and they roll `2`

, `2`

, and `1`

, they would move forward 5 times, to spaces `8`

, `9`

, `10`

, `1`

, and finally stopping on `2`

.

After each player moves, they increase their *score* by the value of the space their pawn stopped on. Players' scores start at `0`

. So, if the first player starts on space `7`

and rolls a total of `5`

, they would stop on space `2`

and add `2`

to their score (for a total score of `2`

). The game immediately ends as a win for any player whose score reaches *at least 1000*.

Since the first game is a practice game, the submarine opens a compartment labeled *deterministic dice* and a 100-sided die falls out. This die always rolls `1`

first, then `2`

, then `3`

, and so on up to `100`

, after which it starts over at `1`

again. Play using this die.

For example, given these starting positions:

+```
Player 1 starting position: 4
+Player 2 starting position: 8
+
```

+This is how the game would go:

+-
+
- Player 1 rolls
`1`

+`2`

+`3`

and moves to space`10`

for a total score of`10`

.
+ - Player 2 rolls
`4`

+`5`

+`6`

and moves to space`3`

for a total score of`3`

.
+ - Player 1 rolls
`7`

+`8`

+`9`

and moves to space`4`

for a total score of`14`

.
+ - Player 2 rolls
`10`

+`11`

+`12`

and moves to space`6`

for a total score of`9`

.
+ - Player 1 rolls
`13`

+`14`

+`15`

and moves to space`6`

for a total score of`20`

.
+ - Player 2 rolls
`16`

+`17`

+`18`

and moves to space`7`

for a total score of`16`

.
+ - Player 1 rolls
`19`

+`20`

+`21`

and moves to space`6`

for a total score of`26`

.
+ - Player 2 rolls
`22`

+`23`

+`24`

and moves to space`6`

for a total score of`22`

.
+

...after many turns...

+-
+
- Player 2 rolls
`82`

+`83`

+`84`

and moves to space`6`

for a total score of`742`

.
+ - Player 1 rolls
`85`

+`86`

+`87`

and moves to space`4`

for a total score of`990`

.
+ - Player 2 rolls
`88`

+`89`

+`90`

and moves to space`3`

for a total score of`745`

.
+ - Player 1 rolls
`91`

+`92`

+`93`

and moves to space`10`

for a final score,`1000`

.
+

Since player 1 has at least `1000`

points, player 1 wins and the game ends. At this point, the losing player had `745`

points and the die had been rolled a total of `993`

times; `745 * 993 = `

.*739785*

Play a practice game using the deterministic 100-sided die. The moment either player wins, *what do you get if you multiply the score of the losing player by the number of times the die was rolled during the game?*