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
n, ans = int(input()), 0
dis, out = set(range(n + 1)), [0] * (n + 1)

for i in range(n, -1, -1):
    if i in dis:
        dis.discard(i)
        tem = ((1 << len(bin(i)[2:])) - 1) ^ i
        if tem in dis:
            dis.discard(tem)
            ans += (tem ^ i) << 1
            out[i] = tem
            out[tem] = i
        else:
            out[i] = i

print('%d\n%s' % (ans, ' '.join(map(str, out))))
