# Palindrome Root

Computer Science Level pending

Most of the positive integers can form a palindrome through the iterative process of repeatedly reversing its digits and adding the resulting numbers. For example, for the number 19,

\begin{aligned} 19 + 91 &= 110 \\ 110+011 &= 121\end{aligned}

can form the palindrome 121 after 2 iterations. In this case, we call 19 the root of palindrome 121. A number $$n$$ is the root of palindrome $$p$$ if it is the smallest number such that after going through some number of iterations the first palindrome it forms is $$p$$.

What is the root of the following number?

4668731596684224866951378664

Clarification:

Although 7 can form 121 after some number of iterations, it is not the root of 121 because the first palindrome formed by it is 55.

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