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+--- Day 9: Encoding Error ---
+
+With your neighbor happily enjoying their video game, you turn your attention to an open data port
+on the little screen in the seat in front of you.
+
+Though the port is non-standard, you manage to connect it to your computer through the clever use of
+several paperclips. Upon connection, the port outputs a series of numbers (your puzzle input).
+
+The data appears to be encrypted with the eXchange-Masking Addition System (XMAS) which,
+conveniently for you, is an old cypher with an important weakness.
+
+XMAS starts by transmitting a preamble of 25 numbers. After that, each number you
+receive should be the sum of any two of the 25 immediately previous numbers. The two numbers will
+have different values, and there might be more than one such pair.
+
+For example, suppose your preamble consists of the numbers 1 through 25 in a random order. To be
+valid, the next number must be the sum of two of those numbers:
+
+- 26 would be a valid next number, as it could be 1 plus 25 (or many other pairs, like
+2 and 24). - 49 would be a valid next number, as it is the sum of 24 and 25. - 100
+would not be valid; no two of the previous 25 numbers sum to 100. - 50 would also
+not be valid; although 25 appears in the previous 25 numbers, the two numbers in the
+pair must be different.
+
+Suppose the 26th number is 45, and the first number (no longer an option, as it is more than 25
+numbers ago) was 20. Now, for the next number to be valid, there needs to be some pair of numbers
+among 1-19, 21-25, or 45 that add up to it:
+
+- 26 would still be a valid next number, as 1 and 25 are still within the previous 25
+numbers. - 65 would not be valid, as no two of the available numbers sum to it. - 64
+and 66 would both be valid, as they are the result of 19+45 and 21+45 respectively.
+
+Here is a larger example which only considers the previous 5 numbers (and has a
+preamble of length 5):
+
+35 20 15 25 47 40 62 55 65 95 102 117 150 182 127 219 299 277 309 576
+
+In this example, after the 5-number preamble, almost every number is the sum of two of the previous
+5 numbers; the only number that does not follow this rule is 127.
+
+The first step of attacking the weakness in the XMAS data is to find the first number in the list
+(after the preamble) which is not the sum of two of the 25 numbers before it.
+What is the first number that does not have this property?
+
+