Little penguin Polo likes permutations. But most of all he likes permutations of integers from 0 to n, inclusive.

For permutation p = p0, p1, ..., pn, Polo has defined its beauty — number <image>.

Expression <image> means applying the operation of bitwise excluding "OR" to numbers x and y. This operation exists in all modern programming languages, for example, in language C++ and Java it is represented as "^" and in Pascal — as "xor".

Help him find among all permutations of integers from 0 to n the permutation with the maximum beauty.

Input

The single line contains a positive integer n (1 ≤ n ≤ 106).

Output

In the first line print integer m the maximum possible beauty. In the second line print any permutation of integers from 0 to n with the beauty equal to m.

If there are several suitable permutations, you are allowed to print any of them.

Examples

Input

4


Output

20
0 2 1 4 3
import java.util.Scanner;

public class C {
    public static long result=0;
    /**
     * @param args
     */
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        Scanner s=new Scanner(System.in);
        int n=s.nextInt();
        int arr[]=new int[n+1];
        func(arr,0,n);
        System.out.println(result);
        System.out.print(arr[0]);
        for(int j=1;j<=n;j++)System.out.print(" "+arr[j]);
        System.out.println();
        s.close();

    }

    private static void func(int[] arr, int b, int e) {
        // TODO Auto-generated method stub
        if(b>=e)return;
        int i=1;
        while(i-1<e)i=(i<<1);
        for(int j=e;j>=i-1-e;j--){
            arr[j]=i-1-j;
            result+=i-1;
        }
        func(arr,b,i-1-e-1);
    }
    
}