Game of Stones

题意翻译

有N堆石子，每次可以从一堆石子中取出若干个石子，但是不能两次从同一堆石子中取出同样数量的石子。问后手是否有必胜策略。1≤N≤10^6，每堆石子数量≤60。

题目描述

Sam has been teaching Jon the Game of Stones to sharpen his mind and help him devise a strategy to fight the white walkers. The rules of this game are quite simple: - The game starts with $ n $ piles of stones indexed from $ 1 $ to $ n $ . The $ i $ -th pile contains $ s_{i} $ stones. - The players make their moves alternatively. A move is considered as removal of some number of stones from a pile. Removal of $ 0 $ stones does not count as a move. - The player who is unable to make a move loses. Now Jon believes that he is ready for battle, but Sam does not think so. To prove his argument, Sam suggested that they play a modified version of the game. In this modified version, no move can be made more than once on a pile. For example, if $ 4 $ stones are removed from a pile, $ 4 $ stones cannot be removed from that pile again. Sam sets up the game and makes the first move. Jon believes that Sam is just trying to prevent him from going to battle. Jon wants to know if he can win if both play optimally.

输入输出格式

输入格式

First line consists of a single integer $ n $ ( $ 1<=n<=10^{6} $ ) — the number of piles. Each of next $ n $ lines contains an integer $ s_{i} $ ( $ 1<=s_{i}<=60 $ ) — the number of stones in $ i $ -th pile.

输出格式

Print a single line containing "YES" (without quotes) if Jon wins, otherwise print "NO" (without quotes)

输入输出样例

输入样例 #1

1
5

输出样例 #1

NO

输入样例 #2

2
1
2

输出样例 #2

YES

说明

In the first case, Sam removes all the stones and Jon loses. In second case, the following moves are possible by Sam:  In each of these cases, last move can be made by Jon to win the game as follows: