24 Game

题意翻译

你有一个整数序列，包括 $n$ 个整数 $1\sim n$。你每次可以从其中拿出两个数 $a,b$，将这两个数从序列中删除，并将 $a+b$、$a-b$ 或 $a\times b$ 放入这个序列。 经过 $n-1$ 次操作后，序列中只会剩下一个数，若这个数可能为 $24$，输出 `YES` 与构造方案，否则，输出 `NO`。

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

题意翻译

你有一个整数序列，包括 $n$ 个整数 $1\sim n$。你每次可以从其中拿出两个数 $a,b$，将这两个数从序列中删除，并将 $a+b$、$a-b$ 或 $a\times b$ 放入这个序列。 经过 $n-1$ 次操作后，序列中只会剩下一个数，若这个数可能为 $24$，输出 `YES` 与构造方案，否则，输出 `NO`。