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

For permutation p = p ₀, p ₁, ..., p _n , Polo has defined its beauty — number .

Expression 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.

输入描述:

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

输出描述:

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.

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