AKOJ-3739:Polo the Penguin and XOR operation

金币值：2 定数：1 时间限制：2.000 s 内存限制：256 M

正确：0 提交：0 正确率：0.00% 命题人：

点赞量：0 收藏量：0 题目类型：程序

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

For permutation p=p₀,p₁,...,p_n, Polo has defined its beauty − number $\text{[math]}$ .

Expression $\text{[math]}$ 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

Output

20
0 2 1 4 3

3739: Polo the Penguin and XOR operation

题目描述