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:
mod = 1000000007
eps = 10**-9


def main():
    import sys
    input = sys.stdin.readline

    N = bin(int(input()))[2:]
    ans = [100, 100] + list(range(1, len(N))) + list(range(1, len(N)))
    k = len(N)
    for i in range(len(N) - 1):
        if N[-i-1] == "1":
            for j in range(len(ans)):
                if ans[j] == i+1:
                    ans.insert(j, k)
                    k += 1
                    break
    ans += list(range(k-1, len(N) - 1, -1))
    print(len(ans))
    print(*ans)


if __name__ == '__main__':
    main()