A tree consists of n nodes numbered from 0 to n-1. Some leaf nodes contain a single coin. Two players take turns. In each move, a player picks a coin from any leaf and slides it one step toward the root (along the unique parent edge). If a coin reaches node 0 (the root), it is removed from the game. The player who makes the last move — the one who moves the final coin to the root — wins.

Both players play optimally. Determine whether the first player can force a win.