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 bitnum(x):
    cnt = 0
    while x:
        cnt += 1
        x >>= 1
    return cnt
def getnext(x):
    bx = bitnum(x)
    if bx == 0:
        return 0,1
    return x^((1<<bx)-1),(1<<(bx-1))
m = int(raw_input())
p = [-1 for i in range(m+1)]
ans = 0
cm = m
while m >= 0:
    pindex = m
    ns,ne = getnext(m)
    #print "next is:", ns, ne
    for i in range(ns, ne):
        p[pindex] = i
        p[i] = pindex
        ans += 2*(i^pindex)
        pindex -= 1
    m = ns - 1
print ans
for i in range(cm):
    print "%d " % p[i],
print p[cm]
