Problem:
Score : 1000 points

Problem Statement

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.

Sample Input 1

7

Sample Output 1

4
1 1 1 1

There are two good strings that appear as subsequences of s: (1,1) and (1,1,1,1). There are six occurrences of (1,1) and one occurrence of (1,1,1,1), for a total of seven.

Sample Input 2

299

Sample Output 2

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 C (GCC 5.4.1) (judge verdict: Accepted)

int mn, mx, cnt, a[99], b[99], i;
f(long n) {
	if (n == 1) return mn = 1;
	int tt = n & 1 ? f(n ^ 1), --mn : (f(n >> 1), ++mx);
	a[i++] = tt;
}

long n;
int j;
int main() {
	scanf("%ld", &n), f(n + 1);
	printf("%d\n", i * 2);
	for (; j < i;) b[a[j++] - mn] = j;
	for (j = 0; j < i;) printf("%d ", b[j++]);
	for (i = 0; i <= mx - mn;) printf("%d ", ++i);
}