# 2005. Subtree Removal Game with Fibonacci Tree

## Description

A **Fibonacci** tree is a binary tree created using the order function `order(n)`

:

`order(0)`

is the empty tree.`order(1)`

is a binary tree with only**one node**.`order(n)`

is a binary tree that consists of a root node with the left subtree as`order(n - 2)`

and the right subtree as`order(n - 1)`

.

Alice and Bob are playing a game with a **Fibonacci** tree with Alice staring first. On each turn, a player selects a node and removes that node **and** its subtree. The player that is forced to delete `root`

loses.

Given the integer `n`

, return `true`

if Alice wins the game or `false`

if Bob wins, assuming both players play optimally.

A subtree of a binary tree `tree`

is a tree that consists of a node in `tree`

and all of this node's descendants. The tree `tree`

could also be considered as a subtree of itself.

**Example 1:**

Input:n = 3Output:trueExplanation:Alice takes the node 1 in the right subtree. Bob takes either the 1 in the left subtree or the 2 in the right subtree. Alice takes whichever node Bob doesn't take. Bob is forced to take the root node 3, so Bob will lose. Return true because Alice wins.

**Example 2:**

Input:n = 1Output:falseExplanation:Alice is forced to take the root node 1, so Alice will lose. Return false because Alice loses.

**Example 3:**

Input:n = 2Output:trueExplanation:Alice takes the node 1. Bob is forced to take the root node 2, so Bob will lose. Return true because Alice wins.

**Constraints:**

`1 <= n <= 100`