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D - At Most 3 (Contestant ver.)

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.

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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:

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

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6

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 $6$.

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12

6
2 5 1 2 5 1

You may prepare multiple weights with the same mass.