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You have a blackboard and initially only an odd number $x$ is written on it. Your goal is to write the number $1$ on the blackboard.

You may write new numbers on the blackboard with the following two operations.

• You may take two numbers (not necessarily distinct) already on the blackboard and write their sum on the blackboard. The two numbers you have chosen remain on the blackboard.
• You may take two numbers (not necessarily distinct) already on the blackboard and write their bitwise XOR on the blackboard. The two numbers you have chosen remain on the blackboard.

Perform a sequence of operations such that at the end the number $1$ is on the blackboard.

你有一块黑板，初始时黑板上仅写有一个奇数 $x$。你的目标是在黑板上写出数字 $1$。

你可以通过以下两种操作在黑板上写下新的数字：

• 任取黑板上已有的两个数（可以相同），将它们的和写在黑板上；被选取的两个数仍保留在黑板上。
• 任取黑板上已有的两个数（可以相同），将它们的按位异或（XOR）写在黑板上；被选取的两个数仍保留在黑板上。

请执行一系列操作，使得最终黑板上出现数字 $1$。

The single line of the input contains the odd integer $x$ ($3 \le x \le 999,999$).

输入仅包含一个奇整数 $x$（$3 \le x \le 999{,}999$）。

Print on the first line the number $q$ of operations you perform. Then $q$ lines should follow, each describing one operation.

• The "sum" operation is described by the line "$a$ + $b$", where $a, b$ must be integers already present on the blackboard.
• The "xor" operation is described by the line "$a$ ^ $b$", where $a, b$ must be integers already present on the blackboard.

The operation symbol (+ or ^) must be separated from $a, b$ by a whitespace.

You can perform at most $100,000$ operations (that is, $q\le 100,000$) and all numbers written on the blackboard must be in the range $[0, 5\cdot10^{18}]$. It can be proven that under such restrictions the required sequence of operations exists. You can output any suitable sequence of operations.

第一行输出你执行的操作次数 $q$。随后输出 $q$ 行，每行描述一次操作。

• “求和”操作表示为一行：“$a$ + $b$”，其中 $a, b$ 必须是黑板上已有的整数。
• “异或”操作表示为一行：“$a$ ^ $b$”，其中 $a, b$ 必须是黑板上已有的整数。

运算符（+ 或 ^）必须与 $a$、$b$ 之间用空格分隔。

你最多可执行 $100{,}000$ 次操作（即 $q\le 100{,}000$），且黑板上所有数字必须在区间 $[0, 5\cdot10^{18}]$ 内。可以证明，在上述限制条件下，所要求的操作序列一定存在。你可以输出任意一个满足条件的操作序列。