# 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.