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Contest: Task: Related: TaskC TaskE

Score : $400$ points

Problem Statement

You are given an integer $W$.
You are going to prepare some weights so that all of the conditions below are satisfied.

  • The number of weights is between $1$ and $300$, inclusive.
  • Each weight has a mass of positive integer not exceeding $10^6$.
  • Every integer between $1$ and $W$, inclusive, is a good integer. Here, a positive integer $n$ is said to be a good integer if the following condition is satisfied:
    • We can choose at most $3$ different weights from the prepared weights with a total mass of $n$.

Print a combination of weights that satisfies the conditions.

Constraints

  • $1 \leq W \leq 10^6$
  • $W$ is an integer.

Input

Input is given from Standard Input in the following format:

$W$

Output

Print in the following format, where $N$ is the number of weights and $A_i$ is the mass of the $i$-th weight. If multiple solutions exist, printing any of them is accepted.

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

Here, $N$ and $A_1,A_2,\dots,A_N$ should satisfy the following conditions:

  • $1 \leq N \leq 300$
  • $1 \leq A_i \leq 10^6$

Sample Input 1

6

Sample Output 1

3
1 2 3

In the output above, $3$ weights with masses $1$, $2$, and $3$ are prepared.
This output satisfies the conditions. Especially, regarding the $3$-rd condition, we can confirm that every integer between $1$ and $W$, inclusive, is a good integer.

  • If we choose only the $1$-st weight, it has a total mass of $1$.
  • If we choose only the $2$-nd weight, it has a total mass of $2$.
  • If we choose only the $3$-rd weight, it has a total mass of $3$.
  • If we choose the $1$-st and the $3$-rd weights, they have a total mass of $4$.
  • If we choose the $2$-nd and the $3$-rd weights, they have a total mass of $5$.
  • If we choose the $1$-st, the $2$-nd, and the $3$-rd weights, they have a total mass of $6$.

Sample Input 2

12

Sample Output 2

6
2 5 1 2 5 1

You may prepare multiple weights with the same mass.