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>
#define ll long long
using namespace std;
ll n;
int l[1005],r[1005];
int p1,p2,now;
void solve(ll x)
{
    //cout<<x<<endl;
    if(x==1)return ;
    if(x%2==1)l[++p1]=++now,x--;
    r[++p2]=++now;
    solve(x/2);
}
int main()
{
    cin>>n;
    solve(n+1);
    printf("%d\n",now*2);
    for(int i=1;i<=p1;i++)cout<<now-l[i]+1<<' ';
    for(int i=p2;i>=1;i--)cout<<now-r[i]+1<<' ';
    for(int i=1;i<=now;i++)cout<<i<<' ';
    return 0;
}