Integer solutions of polynomials

Let $P(x)$ be a polynomial with integer coefficients. Suppose there exist integers $x_1$, $x_2$, $x_3$ such that $$P(x_1) = 2025, \quad P(x_2) = 2026, \quad P(x_3) = 2027.$$ At most how many integer roots does the equation $P(x) = 2029$ have?