The binary tree above has a height of 2 and has 4 leaves. You are going to pass down a ball from the root (the topmost node). Every node other than the leaves has a switch. If a node is *switched off*, the ball will pass to its left child; if a node is *switched on*, the ball will pass to its right child. After passing the ball, the switch will toggle (if it's *on* it becomes *off* and vice versa). Initially, every node is switched off.

Chris built a similar tree of height 100 with the same indexing. Which leaf will contain the \(3366^\text{th}\) ball?

Output you answer modulo 1000.

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