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:
#!/usr/bin/env python3

def construct(N):
    for n in range(40, -1, -1):
        if N >= (1 << n) - 1:
            break
    p = []
    for i in range(1, n+1):
        p.append(i)
    N -= (1 << n) - 1
    for i in range(n-1, -1, -1):
        if N < 1 << i:
            continue
        n += 1
        p = p[:i] + [n] + p[i:]
        N -= 1 << i
    return p

N = int(input())
part = construct(N)
ans = part + [x + 1 for x in range(len(part))]
print(len(ans))
print(*ans, end=' ')
print()