# ---
# title: 292. Nim Game
# id: problem292
# author: Tian Jun
# date: 2020-10-31
# difficulty: Easy
# categories: Brainteaser, Minimax
# link: <https://leetcode.com/problems/nim-game/description/>
# hidden: true
# ---
# 
# You are playing the following Nim Game with your friend:
# 
#   * Initially, there is a heap of stones on the table.
#   * You and your friend will alternate taking turns, and **you go first**.
#   * On each turn, the person whose turn it is will remove 1 to 3 stones from the heap.
#   * The one who removes the last stone is the winner.
# 
# Given `n`, the number of stones in the heap, return `true` _if you can win the
# game assuming both you and your friend play optimally, otherwise
# return_`false`.
# 
# 
# 
# **Example 1:**
# 
#     
#     
#     Input: n = 4
#     Output: false
#     Explanation: These are the possible outcomes:
#     1. You remove 1 stone. Your friend removes 3 stones, including the last stone. Your friend wins.
#     2. You remove 2 stones. Your friend removes 2 stones, including the last stone. Your friend wins.
#     3. You remove 3 stones. Your friend removes the last stone. Your friend wins.
#     In all outcomes, your friend wins.
#     
# 
# **Example 2:**
# 
#     
#     
#     Input: n = 1
#     Output: true
#     
# 
# **Example 3:**
# 
#     
#     
#     Input: n = 2
#     Output: true
#     
# 
# 
# 
# **Constraints:**
# 
#   * `1 <= n <= 231 - 1`
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
