Uolevi has developed a new programming language, that only contains one variable $X$. Initially, the value of $X$ is $1$. In addition, there are three commands:

• ADD: increase $X$ by 3
• MUL: multiply $X$ by 2
• END: print $X$ and stop the program

Your task is to find the shortest program that prints a given number $n$, or state that no such program exists.

Input

The only input line contains an integer $n$.

Output

If a program exists, you should first output the number of commands in it, and after that, each command in a separate line. If there are several possible programs, you can output any of them.

If a program doesn't exist, you should only print $0$.

Example 1

Input:

10

Output:

4
MUL
ADD
MUL
END

Example 2

Input:

12

Output:

0

Subtask 1 (21 points)

• $1 \le n \le 100$

Subtask 2 (37 points)

• $1 \le n \le 10^6$

Subtask 3 (42 points)

• $1 \le n \le 10^{18}$