24 Game

题意翻译

# 题目描述 小X一直很喜欢一个纸牌游戏:“24点”,但最近他发现这个游戏太简单了,所以他发明了一个新游戏。 你有一个整数序列,包括n个整数:1,2,3,...,n。步骤很简单,你可以从其中拿出两个数,我们假设它们是a和b,将这两个数从序列中删除,并将a+b、a-b或a×b放入这个序列。 经过n−1次操作后,序列中只会剩下一个数,你能把这个数变成是24吗? # 输入输出格式 ## 输入格式 一行,包括一个数n。 输出格式 如果可以经过操作计算出24,那么在第一行输出"YES",否则输出"NO"。 在可以的前提下,接下来的n−1行中,每行输出一个计算操作,形如"$a\ op\ b\ =\ c$",a和b表示你选择的数,而op,则是你使用的计算符号(加、减或乘)。算式中$abs(c)$不会超过(绝对值)$10^{18}$,请注意输出的每个算式的字符与数字之间必须有空格。 如果你有多种解决的办法,输出任意一个即可 Translated by lonelysir

题目描述

Little X used to play a card game called "24 Game", but recently he has found it too easy. So he invented a new game. Initially you have a sequence of $ n $ integers: $ 1,2,...,n $ . In a single step, you can pick two of them, let's denote them $ a $ and $ b $ , erase them from the sequence, and append to the sequence either $ a+b $ , or $ a-b $ , or $ a×b $ . After $ n-1 $ steps there is only one number left. Can you make this number equal to $ 24 $ ?

输入输出格式

输入格式


The first line contains a single integer $ n $ $ (1<=n<=10^{5}) $ .

输出格式


If it's possible, print "YES" in the first line. Otherwise, print "NO" (without the quotes). If there is a way to obtain $ 24 $ as the result number, in the following $ n-1 $ lines print the required operations an operation per line. Each operation should be in form: " $ a $ $ op $ $ b $ = $ c $ ". Where $ a $ and $ b $ are the numbers you've picked at this operation; $ op $ is either "+", or "-", or "\*"; $ c $ is the result of corresponding operation. Note, that the absolute value of $ c $ mustn't be greater than $ 10^{18} $ . The result of the last operation must be equal to $ 24 $ . Separate operator sign and equality sign from numbers with spaces. If there are multiple valid answers, you may print any of them.

输入输出样例

输入样例 #1

1

输出样例 #1

NO

输入样例 #2

8

输出样例 #2

YES
8 * 7 = 56
6 * 5 = 30
3 - 4 = -1
1 - 2 = -1
30 - -1 = 31
56 - 31 = 25
25 + -1 = 24