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
import math


def solve():
    n, = map(int, input().split())
    top = 1
    while top <= n:
        top *= 2
    top -= 1

    ans = [0] * (n + 1)
    i = n
    cur = n
    while i > 0:
        if top - i > cur:
            cur = i
            top = 1
            while top <= cur:
                top *= 2
            top -= 1
        ans[i] = top - i
        ans[top - i] = i
        i -= 1
    score = 0
    if n % 2 == 1:
        ans[top] = 0
        ans[0] = top
    for i in range(n + 1):
        score += ans[i] ^ i

    print(score)
    print(*ans)


if __name__ == "__main__":
    t = 1
    # t = int(input())
    for _ in range(t):
        solve()
