Dividing the numbers

Description:

Input:

The first line contains a single integer n (2 ≤ n ≤ 60 000) — the number of integers Petya has.

Output:

Print the smallest possible absolute difference in the first line.

In the second line print the size of the first group, followed by the integers in that group. You can print these integers in arbitrary order. If there are multiple answers, print any of them.

Sample Input:

4

Sample Output:

0
2 1 4 

Sample Input:

2

Sample Output:

1
1 1 

Note:

In the first example you have to put integers 1 and 4 in the first group, and 2 and 3 in the second. This way the sum in each group is 5, and the absolute difference is 0.

In the second example there are only two integers, and since both groups should be non-empty, you have to put one integer in the first group and one in the second. This way the absolute difference of sums of integers in each group is 1.