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:
def ncr(n, r):
    r = min(n - r, r)
    up = 1
    down = 1
    for i in range(r):
        up *= (n - i)
        down *= (i + 1)
    return up // down


def seq(x):
    s = 0
    for i in range(1, x):
        j = i * 2
        if j > x:
            break
        s += ncr(x, j)
    return s


def ins(total, p):
    s = 0
    for i in range(p + 1):
        s += ncr(p, i) * ncr(total - p, i)
    return s

ans = []
N = int(input())
k = 1

for i in range(41, 0, -1):
    x = seq(i)
    if N >= x:
        for j in range(i):
            ans.append(k)
        N -= x
        k += 1
        break

size = len(ans)
s = size // 2
while N > 90:
    m = 0
    t = 0
    for i in range(s + 1):
        tmp = ins(size, i)
        if tmp > N:
            break
        if tmp > t:
            t = tmp
            m = i
    N -= t
    ans.insert(m, k)
    ans.append(k)
    k += 1

while N > 0:
    for i in range(41, 0, -1):
        x = seq(i)
        if N >= x:
            for j in range(i):
                ans.append(k)
            N -= x
            k += 1
            break
print(len(ans))
print(" ".join([str(x) for x in ans]))