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 deque

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

"""左右で文字列集合を分割する。abc bac のように、左側、右側のそれぞれでは
文字が重複しないようにして作る。"""

def f(N, i=1):
    # i 以上の整数を使う
    if N == 1:
        return deque(), deque()
    if N % 2 == 0:
        A, B = f(N // 2, i + 1)
        A.append(i)
        B.append(i)
        return A, B
    else:
        A, B = f(N - 1, i + 1)
        A.append(i)
        B.appendleft(i)
        return A, B

N = int(read()) + 1

A, B = f(N)
S = A + B
print(len(S))
print(*S)