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 ones(n): 
    number_of_bits = (int)(math.floor(math.log(n) /
                                math.log(2))) + 1;   
    return [((1 << number_of_bits) - 1) ^ n,(1 << number_of_bits) - 1]; 
n = int(input())
has=[0]*(n+1)
ans=[0]*(n+1)
fin=0
for i in range(n,0,-1):
    if has[i]==0:
        com,fi = ones(i)
#        print(com,fi,i)
        has[com]=1
        fin+=2*fi
        ans[com]=i
        ans[i]=com
print(fin)
print(*ans)


