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 CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
int a[210],b[210],la,lb,i=100;
int main()
{
    long long n;
    scanf("%lld",&n);
    n++;
    while(n>1)
    {
        if(n&1)n--,a[++la]=i--;
        else n>>=1,b[++lb]=i--;
    }
    printf("%d\n",(la+lb)*2);
    for(int j=1;j<=la;j++)
        printf("%d ",a[j]-i);
    for(int j=lb;j>=1;j--)
        printf("%d ",b[j]-i);
    for(int j=100-la-lb+1;j<100;j++)
        printf("%d ",j-i);
    printf("%d\n",100-i);
    return 0;
}