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 .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.

Input The single line contains a positive integer n (1 \le n \le 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.