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.io.*;
import	java.util.*;
public	class	Main{
	public	static	void	main(String[]args){
		Scanner	cin=new	Scanner(System.in);
		int	n=1+cin.nextInt(),m,i;
		PrintWriter	out=new	PrintWriter(System.out);
		for(out.println((n-1L)*n);0<n;){
			for(n^=i=m=Integer.highestOneBit(n);n<i;out.print(--i+" "));
			for(;0<i;out.print(--i+m+" "));
		}out.close();
	}
}
