Problem Statement

taiga created the following problem.

GCD Subset

You are given a sequence $A$ of positive integers of length $N$. Here, all elements of $A$ are distinct. A non-empty subset $S=\lbrace S_1,S_2,\dots,S_k \rbrace$ of $\lbrace 1,2, \dots ,N \rbrace$ is called a good set if it satisfies the following condition.

• $\gcd(A_{S_1},A_{S_2},\dots,A_{S_k}) \ge 2$ (where $\gcd(X_1,X_2,\dots,X_k)$ denotes the greatest common divisor of $X_1,X_2,\dots,X_k$.)

There are $2^N-1$ non-empty subsets of $\lbrace 1,2, \dots ,N \rbrace$. Find the number of good sets among them, modulo $998244353$.

You are given an integer $M$. Output $1$ sequence $A$ for which the answer to the problem "GCD Subset" is $M$.

Input

$M$

Output

Output the length $N$ of the sequence on line $1$ and the sequence $A$ on line $2$, as shown below. If there are multiple valid answers, any of them will be accepted.

$N$
$A_1$ $A_2$ $\dots$ $A_N$

The output must also satisfy the following constraints.

Output Constraints

Sample

3

3
1 3 6

3
1
3
6