P5863 [SEERC 2018] Numbers

A palindromic number is an integer that reads the same when written normally and when written in reverse. For example, the numbers $142241$ and $102201$ are palindromic, but the numbers $1023401$ and $10510$ are not. You want to decompose a number $n$ into a sum of two palindromic numbers. Please compute the number of ways to decompose it in this form.

Only one line contains an integer $n \ (1 \leq n \leq 10^{18})$.

Output an integer representing the number of ways to decompose $n$ as the sum of two palindromic numbers.

In the first sample, the decompositions are: $(5, 151), (55, 101), (101, 55), (151, 5)$. In the second sample, the decompositions are: $(515, 9009), (636, 8888), (8888, 636), (9009, 515)$. In the third sample, the decompositions are: $(33, 42624), (333, 42324), (4884, 37773), (37773, 4884), (42324, 333), (42624, 33)$. Translated by ChatGPT 5