Let λ ∈ R and let the equation E be |x|^2-2|x|+|λ-3|=0. Then the largest element in the set S = {x+λ: x is an integer solution of E } is ____

Let $\displaystyle \lambda \in \mathbb{R}$ and let the equation E be $\displaystyle |x|^2-2|x|+|\lambda-3|=0$. Then the largest element in the set $\displaystyle \mathrm{S}=$ $\displaystyle \{x+\lambda: x$ is an integer solution of E$\displaystyle \}$ is $\displaystyle \_\_\_\_$