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 sys
import math

def solve(n, data):
    n += 1
    if n==0:
        return data
    base = math.log(n, 2)
    if (base != int(base)):
        base = int(base) + 1
    else:
        base = int(base)

    base = 2**base
    diff = base - n - 1
    
    for ind in xrange(n):
        #print str(ind) + ">>" + str(base - ind - 1)
        data[ind] = base - ind - 1
    #print data
    #print ("n=" + str(n) + " base=" + str(base) + " diff=" + str(diff))
    #recur
    solve(diff, data)
    return data

n = int(sys.stdin.readline())

data = [0]*(n+1)
solve(n, data)
#calc sum
summ = 0
for ind in xrange(len(data)):
    summ += ind | data[ind]
print str(summ)
print ' '.join(map(str, data))

