 Day 15: Rambunctious Recitation 
You catch the airport shuttle and try to book a new flight to your vacation island. Due to the storm, all direct flights have been cancelled, but a route is available to get around the storm. You take it.
+While you wait for your flight, you decide to check in with the Elves back at the North Pole. They're playing a memory game and are ever so excited to explain the rules!
+In this game, the players take turns saying numbers. They begin by taking turns reading from a list of starting numbers (your puzzle input). Then, each turn consists of considering the most recently spoken number:
+
+
 If that was the first time the number has been spoken, the current player says
0
.
+  Otherwise, the number had been spoken before; the current player announces how many turns apart the number is from when it was previously spoken. +
So, after the starting numbers, each turn results in that player speaking aloud either 0
(if the last number is new) or an age (if the last number is a repeat).
For example, suppose the starting numbers are 0,3,6
:

+
 Turn 1: The
1
st number spoken is a starting number,0
.
+  Turn 2: The
2
nd number spoken is a starting number,3
.
+  Turn 3: The
3
rd number spoken is a starting number,6
.
+  Turn 4: Now, consider the last number spoken,
6
. Since that was the first time the number had been spoken, the4
th number spoken is0
.
+  Turn 5: Next, again consider the last number spoken,
0
. Since it had been spoken before, the next number to speak is the difference between the turn number when it was last spoken (the previous turn,4
) and the turn number of the time it was most recently spoken before then (turn1
). Thus, the5
th number spoken is4  1
,3
.
+  Turn 6: The last number spoken,
3
had also been spoken before, most recently on turns5
and2
. So, the6
th number spoken is5  2
,3
.
+  Turn 7: Since
3
was just spoken twice in a row, and the last two turns are1
turn apart, the7
th number spoken is1
.
+  Turn 8: Since
1
is new, the8
th number spoken is0
.
+  Turn 9:
0
was last spoken on turns8
and4
, so the9
th number spoken is the difference between them,4
.
+  Turn 10:
4
is new, so the10
th number spoken is0
.
+
(The game ends when the Elves get sick of playing or dinner is ready, whichever comes first.)
+Their question for you is: what will be the 2020
th number spoken? In the example above, the 2020
th number spoken will be 436
.
Here are a few more examples:
+
+
 Given the starting numbers
1,3,2
, the2020
th number spoken is1
.
+  Given the starting numbers
2,1,3
, the2020
th number spoken is10
.
+  Given the starting numbers
1,2,3
, the2020
th number spoken is27
.
+  Given the starting numbers
2,3,1
, the2020
th number spoken is78
.
+  Given the starting numbers
3,2,1
, the2020
th number spoken is438
.
+  Given the starting numbers
3,1,2
, the2020
th number spoken is1836
.
+
Given your starting numbers, what will be the 2020
th number spoken?