# Smallest Inequality Bound

**Algebra**Level 5

What is the smallest integer \(N\) such that \( \left( \sqrt{ x^4 - 3x^2 - 6x +13} - \sqrt{x^4 - x^2 +1 } \right) ^4 < N\), as \( x \) ranges over all real values?

Note: There is a strict inequality in the challenge.

**Details and assumptions**

If you think that the expression can take values over 999, input your answer as 999.