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.*;
public class Main {
public static void main(String [] args){
	Scanner in=new Scanner(System.in);
	int n=in.nextInt();
	int array[]=new int[n+1];
	int keep=n;
	while(n > 0){
	int temp=Integer.highestOneBit(n);
	int val=temp-1;	
	   for(int i=temp;i<=n;i++){
	   array[i]=val;
	   array[val]=i;
	   val--;
	   }
	   n=val;
	}
	long ans=0;
	StringBuilder sb=new StringBuilder();
	for(int i=0;i<=keep;i++)ans+=array[i]^i;
	System.out.println(ans);
	for(int i=0;i<=keep;i++)sb.append(array[i]+" ");
	System.out.print(sb);
}
}