Problem Statement

Define $f(x)$ as the sum of the positive divisors of $x$, and $a \oplus b$ as the bitwise XOR of $a$ and $b$.

You are given a non-negative integer $N$. Construct $1$ sequence of positive integers $A = (A_1, A_2, \ldots, A_M)$ that satisfies the following conditions.

• $1 \le M \le 100$
• $f(A_1) \oplus f(A_2) \oplus \cdots \oplus f(A_M) = N$
• $A_1 + A_2 + \cdots + A_M \lt 2 \times N$
• The elements of $A$ are pairwise distinct

However, if no $A$ satisfying the conditions exists, output $-1$.

Input

$N$

• $N$ is an integer
• $0\le N\le 10^{12}$

Output

If an $A$ satisfying the conditions exists, output it in the following format.

$M$
$A_1$ $A_2$ $\cdots$ $A_M$

If no $A$ satisfying the conditions exists, output $-1$ on a single line.

Sample

17

3
1 6 12

0

-1