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:
import sys
from collections import Counter
readline = sys.stdin.readline

A = [0]
dp = [0]
N = int(readline())

cnt = 0
while N:
    cnt += 1
    idx = len(A)
    if N >= 1+dp[-1]:
        N -= 1+dp[-1]
        A.append(cnt)
        dp.append(1+2*dp[-1])
    else:
        for l in range(len(A)):
            if N >= dp[l] + 1:
                idx = l
    
        N -= dp[idx] + 1
        dp = dp[:idx+1] + [2*dp[idx]+1] + [dp[idx]+1 + dp[i] for i in range(idx+1, len(dp))]
        A = A[:idx+1] + [cnt] + A[idx+1:]

ans = (A[1:] + list(range(1, len(A))))
print(len(ans))
print(*ans)