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 PYTHON):

Solution:
from sys import stdin
while True:
    s = stdin.readline()
    if not s:
        break
    n = int(s)
    a = [] 
    b = []
    f = []
    for i in xrange(60):
        f.append(2**i)
    bi = [] 
    s = 0 
    cur = 59 
    while cur>=0:
        if f[cur ]-1 <=n:
            break 
        cur -= 1 
    hi = cur
    done = 2**hi - 1 
    for u in xrange(1,hi+1):
        b.append(u)
    co = 1 
    nn = n 
    n -= done 
    while cur >=1 :
        a.append(cur)
        if f[cur-1]<= n:
            hi += 1 
            a.append(hi)
            b.append(hi)
            n-= f[cur-1]
        
        cur -=1 
    a.reverse()
    c =  a + b 
    print  len(c)
    for i in c:
        print i,
    print ""