Problem Statement

Snuke has integers $x$ and $y$. Initially, $x=0,y=0$.

Snuke can do the following four operations any number of times in any order:

• Operation $1$: Replace the value of $x$ with $x+1$.
• Operation $2$: Replace the value of $y$ with $y+1$.
• Operation $3$: Replace the value of $x$ with $x+y$.
• Operation $4$: Replace the value of $y$ with $x+y$.

You are given a positive integer $N$. Do at most $130$ operations so that $x$ will have the value $N$. Here, $y$ can have any value. We can prove that such a sequence of operations exists under the constraints of this problem.

Constraints

• $1 \leq N \leq 10^{18}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N

Output

Print your answer in the following format:

K
t_1
t_2
\vdots
t_K

Here, $K$ $(0 \leq K \leq 130)$ denotes the number of operations, and $t_i$$(1 \leq t_i \leq 4)$ represents the $i$-th operation to be done.