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 PYTHON3):

Solution:
if __name__ == "__main__":
    N = int(input())
    n = 40
    for i in range(40, -1, -1):
        if (N >= (1 << i) - 1):
            n = i
            break
    data = []
    for i in range(n):
        data.append(i + 1)
    N -= (1 << n) - 1
    tmp = n
    for i in range(n - 1, -1, -1):
        if (N < (1 << i)):
            continue
        tmp += 1
        data = data[:i] + [tmp] + data[i:]
        N -= (1 << i)
    ans = []
    for x in range(len(data)):
        ans.append(x + 1)
    ans = ans + data
    print (len(ans))
    print (" ".join(map(str, ans)))