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


def f(num):
	pot = 1
	while(pot<(num+1)):
		pot<<=1
	if (num==pot-1):
		for i in xrange(num,-1,-1):
			yield i
		return
	delta = num-(pot>>1)+1
	for i in f( (pot>>1)-1-delta):
		yield i
	for i in xrange((pot>>1)-1+delta, (pot>>1)-1-delta,-1):
		yield i





def main():
	num = input()
	l = list(f(num))
	s = sum([i ^ l[i] for i in xrange(num+1)])
	print s
	print ' '.join((str(i) for i in l))




main()