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