A. Mood Balance
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Autumn is a time of changeable moods. Some people are sad about the departing summer, some are happy about the slowly approaching winter, while others simply stroll peacefully and enjoy the autumn freshness and coolness.

When you walk through the autumn alley, you are often visited by deep thoughts about the meaning of life. Every minute, a new thought comes to you, and and you can choose whether it will be a negative thought or an ambiguous one (there are no positive thoughts). If your current mood is represented by the number $$$x$$$ and it is the $$$i$$$-th minute of the walk, then

  • a negative thought decreases your mood by $$$1$$$, making it $$$x - 1$$$;
  • an ambiguous thought first changes Kostya's mood by $$$i - 2$$$, and then doubles it, making it $$$2(x + i - 2)$$$.

Since you enjoy tranquility you want your mood at the end of the walk to be the same as it was at the beginning — zero. You are also not very fond of negative thoughts, so you would like to plan your walk in such a way that there are as few of them as possible.

Plan your thoughts during the walk so that by the end of the journey your mood is $$$0$$$, while minimizing the number of negative thoughts. Your initial mood is $$$x = 0$$$, and the minutes of the walk are numbered from $$$1$$$ to $$$n$$$.

Input

The first and only line contains an integer $$$n$$$ — the duration of the walk in minutes ($$$4 \leq n \leq 10^{18}$$$).

Output

In the first line, output an integer $$$k$$$ — the minimum number of negative thoughts.

In the next line, output $$$k$$$ integers from $$$1$$$ to $$$n$$$ in increasing order — the minutes at which you should choose negative thoughts.

Examples
Input
5
Output
2
1 4
Input
8
Output
1
4