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.

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:

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

Constraints

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

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.

见题面 Input 部分

见题面 Output 部分