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C. Polo the Penguin and XOR operation

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLittle 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.

Input

The single line contains a positive integer *n* (1 ≤ *n* ≤ 10^{6}).

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

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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