*near-symmetric* number if after twenty-five iterations, the resulting integer is still not a palindrome. What is the smallest positive near-symmetric number?

**Details and assumptions**

A palindrome is a number that remains the same when its digits are reversed.

As an explicit example, consider the integer to be $49$. The resulting number will be $49 + 94 = 143$. Repeat: $143 + 341 = 484$, which is a palindrome (after $2 < 25$ iterations). Thus $49$ is not a near-symmetric number.