You are generating data for the second problem of the DMOPC, which reads as follows:

Given an integer array $A$ of length $N$ $(1\le N\le {10}^6)$ with elements in the range $[-{10}^9,{10}^9]$, output the number of non-empty contiguous subarrays with an even sum.

Just as you were about to wrap up the last batch of cases, you open Discord to see 8 pings from Keenan, who insists that the data is weak unless there is a test case where the expected output is $K$. As it is only a few hours before the actual contest, there's no time for you to create such a case by hand. Please write a program to find a case satisfying Keenan's requirement, or determine that his requirement is impossible to satisfy (under the given constraints of the problem).

Constraints

$0\le K\le {10}^{18}$

Subtask 1 [50%]

$0\le K\le {10}^6$

Subtask 2 [50%]

No additional constraints.

Input Specification

The first and only line will contain the integer $K$.

Output Specification

If it is impossible to satisfy Keenan's requirement under the constraints of the problem, output $-1$.

Otherwise, output $N$ $(1\le N\le {10}^6)$ on the first line, representing the length of the array.

Then, on the second line, output $N$ integers $A_i$ $(-{10}^9\le A_i\le {10}^9)$, representing an array of length $N$ that satisfies Keenan's requirement.

If there are multiple arrays satisfying Keenan's requirement, output any one of them.

Sample Input 1

7

Sample Output 1

5
5 4 9 1 6

Explanation for Sample 1

The subarrays with even sum are: $[5,4,9],[4],[4,9,1],[4,9,1,6],[9,1],[9,1,6],[6]$.

Sample Input 2

1000000000000000000

Sample Output 2

-1