Two Piles

You are given $N$ pairs of integers. The $i$-th pair is $(A_i, B_i)$. You also have two piles with you, both initially empty. You will perform the following process: - For each $i$ from $1$ to $N$, choose **exactly one** of $A_i$ or $B_i$. - Then, add the chosen integer to one of your two piles. At the end of the process, both piles **must be non-empty** (i.e, you should have added at least on