Sub-Array With Maximum Sum

Alice has two arrays $A$ and $B$, each of length $N$. She wants an array $C$ of length $2\cdot N$ using both the arrays such that: - Each element of the arrays $A$ and $B$ is used exactly once; - The $i^{th}$ element of array $A$ takes either $(2\cdot i)^{th}$ or $(2\cdot i-1)^{th}$ position in $C$; - The $i^{th}$ element of array $B$ takes either $(2\cdot i)^{th}$ or $(2\cdot i-1)^{th}$ positi