Problem: We will call a string x good if it satisfies the following condition:

* Condition: x can be represented as a concatenation of two copies of another string y of length at least 1.



For example, `aa` and `bubobubo` are good; an empty string, `a`, `abcabcabc` and `abba` are not good.

Eagle and Owl created a puzzle on good strings. Find one string s that satisfies the following conditions. It can be proved that such a string always exists under the constraints in this problem.

* 1 ≤ |s| ≤ 200
* Each character of s is one of the 100 characters represented by the integers 1 through 100.
* Among the 2^{|s|} subsequences of s, exactly N are good strings.

Constraints

* 1 ≤ N ≤ 10^{12}

Input

Input is given from Standard Input in the following format:


N


Output

In the first line, print |s|, the length of s. In the second line, print the elements in s in order, with spaces in between. Any string that satisfies the above conditions will be accepted.

Examples

Input

7


Output

4
1 1 1 1


Input

299


Output

23
32 11 11 73 45 8 11 83 83 8 45 32 32 10 100 73 32 83 45 73 32 11 10

Solution (in CPP):

Solution:
#include <iostream>

using namespace std;
int s[200],pre[100],back[100];
int main()
{
	long long n;
	cin >> n;
	int tmp = 100,r = 1,l = 1;
	while(n)
	{
		if(n & 1)
		{
			n >>= 1;
			back[r ++] = tmp --;
		}
		else
		{
			n --;
			pre[l ++] = tmp --;
		}
	}
	cout << 2 * (100 - tmp) << endl;
	for(int i = 1;i < l;i ++)
		printf("%d ",pre[i]);
	for(int i = r - 1;i > 0;i --)
		printf("%d ",back[i]);
	for(int i = tmp + 1;i < 100;i ++)
		printf("%d ",i);
	cout << 100 << endl;
	return 0;
}