DMOPC '21 Contest 4 P3 - Palindromic Presents
View as PDFPetep is preparing a Christmas present for Reter! As they both love palindromes, Petep decides to gift Reter a set of  distinct non-negative palindromic integers. To make the best possible present, Petep decides that the sum of any subset of these integers (including the sum of all 
 integers) should also be a palindrome, and the sum of the 
 integers should be as small as possible to ensure that they fit under the Christmas tree. Please help Petep find any set of 
 integers satisfying these properties.
Input Specification
There is no input for this problem.
Output Specification
Output  non-negative integers each on its own line, the set of integers in Petep's present.
Scoring
If your output is improperly formatted, the sum of all  integers exceeds 
, the 
 integers are not all distinct, or the sum of any subset of the integers is not a palindrome, you will receive 
 points.
Otherwise, let  be the sum of the 
 integers in your solution, and let 
 be the sum of the 
 integers in the best possible solution.
If , you will receive full points. Otherwise, you will receive a positive number of points based on how close 
 is to 
. It is guaranteed that a solution with a larger 
 will not score more points than a solution with a smaller 
.
Sample Output
2
7
18281
828
4
161
8
0
33
9
Explanation
This output is only provided to clarify the output format. Note that it would score  points because, for example, 
 is not a palindrome.
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