$A+B$ is a problem used to test one's basic knowledge for competitive programming. Here is yet another boring variation of it.

You have two integers, $A$ and $B$. You want to make them equal. To do so, you can perform several steps, where each step is one of the following:

• $A$+= $A$
• $A$+= $B$
• $B$+= $A$
• $B$+= $B$

Unfortunately, $A+B$ is a hard problem for us, so you are allowed to make at most 5000 steps.

Input

Two integers $A, B$ are given. ($1 \le A, B \le 10^{18}$).

Output

In the first line, print a single integer $n$ ($0 \le n \le 5000$) denoting the number of steps.

In next $n$ lines, print one of the following strings to denote your desired operation: "A+=A", "A+=B", "B+=A", or "B+=B".

Any sequence of steps that yields the desired result will be judged correct.

Examples

Input 1

2 3

Output 1

4
B+=B
B+=A
A+=A
A+=A